TPTP Problem File: SLH0619^1.p
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%------------------------------------------------------------------------------
% File : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain : Archive of Formal Proofs
% Problem :
% Version : Especial.
% English :
% Refs : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source : [Des23]
% Names : Combinable_Wands/0003_CombinableWands/prob_00300_011152__7752782_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1417 ( 619 unt; 140 typ; 0 def)
% Number of atoms : 3855 (1172 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 9478 ( 308 ~; 62 |; 193 &;7533 @)
% ( 0 <=>;1382 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 1446 (1446 >; 0 *; 0 +; 0 <<)
% Number of symbols : 136 ( 133 usr; 14 con; 0-4 aty)
% Number of variables : 3328 ( 244 ^;3051 !; 33 ?;3328 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-19 09:09:03.650
%------------------------------------------------------------------------------
% Could-be-implicit typings (7)
thf(ty_n_t__Set__Oset_I_062_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J_J,type,
set_state_state_o: $tType ).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
set_set_set_state: $tType ).
thf(ty_n_t__Set__Oset_I_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
set_o_set_state: $tType ).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_set_state: $tType ).
thf(ty_n_t__Set__Oset_I_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
set_state_o: $tType ).
thf(ty_n_t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
set_state: $tType ).
thf(ty_n_t__PartialHeapSA__Ostate,type,
state: $tType ).
% Explicit typings (133)
thf(sy_c_CombinableWands_Ocwand,type,
cwand: set_state > set_state > set_state ).
thf(sy_c_CombinableWands_Owand,type,
wand: set_state > set_state > set_state ).
thf(sy_c_Complete__Lattices_OInf__class_OInf_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
comple1470863462450220288_state: set_o_set_state > $o > set_state ).
thf(sy_c_Complete__Lattices_OInf__class_OInf_001_062_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
comple3128546889576232729tate_o: set_state_state_o > state > state > $o ).
thf(sy_c_Complete__Lattices_OInf__class_OInf_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
comple6810834910230287260tate_o: set_state_o > state > $o ).
thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
comple1177038664686533161_state: set_set_state > set_state ).
thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
comple2682067033655477471_state: set_set_set_state > set_set_state ).
thf(sy_c_Complete__Partial__Order_Occpo__class_Ofixp_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
comple4794180994860465059_state: ( set_state > set_state ) > set_state ).
thf(sy_c_Conditionally__Complete__Lattices_Opreorder__class_Obdd__below_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
condit9136120872139659296_state: set_set_state > $o ).
thf(sy_c_Finite__Set_OFpow_001t__PartialHeapSA__Ostate,type,
finite_Fpow_state: set_state > set_set_state ).
thf(sy_c_Fun_Omonotone__on_001t__PartialHeapSA__Ostate_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
monoto271350166776559507_state: set_state > ( state > state > $o ) > ( set_state > set_state > $o ) > ( state > set_state ) > $o ).
thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
monoto160555381311970121_state: set_set_state > ( set_state > set_state > $o ) > ( set_state > set_state > $o ) > ( set_state > set_state ) > $o ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
minus_3933957440811877961_state: set_state > set_state > set_state ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
minus_5895981879909142783_state: set_set_state > set_set_state > set_set_state ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
uminus4730887800166984048_state: ( $o > set_state ) > $o > set_state ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
uminus7723173452139699081tate_o: ( state > state > $o ) > state > state > $o ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
uminus3809647891681718284tate_o: ( state > $o ) > state > $o ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
uminus472742206872269241_state: set_state > set_state ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
uminus4035512285888117871_state: set_set_state > set_set_state ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
uminus2384571021370171429_state: set_set_set_state > set_set_set_state ).
thf(sy_c_Inductive_Ocomplete__lattice__class_Ogfp_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
comple8759115402146780658_state: ( set_state > set_state ) > set_state ).
thf(sy_c_Inductive_Ocomplete__lattice__class_Olfp_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
comple5794554108862647415_state: ( set_state > set_state ) > set_state ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
inf_inf_set_state: set_state > set_state > set_state ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
inf_in8939913482472430008_state: set_set_state > set_set_state > set_set_state ).
thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
semila3858001251800985922_state: ( set_state > set_state > set_state ) > set_state > ( set_state > set_state > $o ) > ( set_state > set_state > $o ) > $o ).
thf(sy_c_Lattices_Osup__class_Osup_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
sup_sup_o_set_state: ( $o > set_state ) > ( $o > set_state ) > $o > set_state ).
thf(sy_c_Lattices_Osup__class_Osup_001_062_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
sup_su7525921995284788454tate_o: ( state > state > $o ) > ( state > state > $o ) > state > state > $o ).
thf(sy_c_Lattices_Osup__class_Osup_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
sup_sup_state_o: ( state > $o ) > ( state > $o ) > state > $o ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
sup_sup_set_state: set_state > set_state > set_state ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
sup_su4188871578264421970_state: set_set_state > set_set_state > set_set_state ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
sup_su3277220503338409480_state: set_set_set_state > set_set_set_state > set_set_set_state ).
thf(sy_c_Orderings_Obot__class_Obot_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
bot_bot_o_set_state: $o > set_state ).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
bot_bo3298213311409307006tate_o: state > state > $o ).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
bot_bot_state_o: state > $o ).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Set__Oset_It__PartialHeapSA__Ostate_J_M_Eo_J,type,
bot_bot_set_state_o: set_state > $o ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
bot_bo782247444858010053_state: set_o_set_state ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
bot_bot_set_state_o2: set_state_o ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
bot_bot_set_state: set_state ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
bot_bo2271482359692755898_state: set_set_state ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
bot_bo7389043141884672880_state: set_set_set_state ).
thf(sy_c_Orderings_Oord__class_Oless_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
ord_less_o_set_state: ( $o > set_state ) > ( $o > set_state ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001_062_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
ord_le9065008989417891262tate_o: ( state > state > $o ) > ( state > state > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
ord_less_state_o: ( state > $o ) > ( state > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_I_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
ord_le3245661169210212869_state: set_o_set_state > set_o_set_state > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
ord_less_set_state: set_state > set_state > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
ord_le8280034978549525370_state: set_set_state > set_set_state > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
ord_le6814633228373517104_state: set_set_set_state > set_set_set_state > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
ord_le621814680099590950_state: ( $o > $o > set_state ) > ( $o > $o > set_state ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
ord_le9189382018855386905_state: ( $o > set_state ) > ( $o > set_state ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
ord_le6992062077777787599_state: ( $o > set_set_state ) > ( $o > set_set_state ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
ord_le4344933087531911346tate_o: ( state > state > $o ) > ( state > state > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
ord_less_eq_state_o: ( state > $o ) > ( state > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
ord_le4652835513209282297_state: set_o_set_state > set_o_set_state > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
ord_le2494988322063910608_state: set_state > set_state > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
ord_le5175021213330142598_state: set_set_state > set_set_state > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
ord_le3154822624800881980_state: set_set_set_state > set_set_set_state > $o ).
thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
order_1484864080787882322_state: ( ( $o > set_state ) > $o ) > $o > set_state ).
thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
order_2642746146112740183_state: ( set_state > $o ) > set_state ).
thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
order_6508859784380345869_state: ( set_set_state > $o ) > set_set_state ).
thf(sy_c_Orderings_Oordering__top_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
orderi4116547514405938474_state: ( ( $o > set_state ) > ( $o > set_state ) > $o ) > ( ( $o > set_state ) > ( $o > set_state ) > $o ) > ( $o > set_state ) > $o ).
thf(sy_c_Orderings_Oordering__top_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
ordering_top_state_o: ( ( state > $o ) > ( state > $o ) > $o ) > ( ( state > $o ) > ( state > $o ) > $o ) > ( state > $o ) > $o ).
thf(sy_c_Orderings_Oordering__top_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
orderi2162033302644881791_state: ( set_state > set_state > $o ) > ( set_state > set_state > $o ) > set_state > $o ).
thf(sy_c_Orderings_Oordering__top_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
orderi6282941313354935349_state: ( set_set_state > set_set_state > $o ) > ( set_set_state > set_set_state > $o ) > set_set_state > $o ).
thf(sy_c_Orderings_Opartial__preordering_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
partia1090249825177899695_state: ( ( $o > set_state ) > ( $o > set_state ) > $o ) > $o ).
thf(sy_c_Orderings_Opartial__preordering_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
partia7871104319988624314_state: ( set_state > set_state > $o ) > $o ).
thf(sy_c_Orderings_Opartial__preordering_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
partia4579038784995701360_state: ( set_set_state > set_set_state > $o ) > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
top_top_o_set_state: $o > set_state ).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
top_to5868225466921797218tate_o: state > state > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
top_top_state_o: state > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Set__Oset_It__PartialHeapSA__Ostate_J_M_Eo_J,type,
top_top_set_state_o: set_state > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J_M_Eo_J,type,
top_to8638843179453837305tate_o: set_set_state > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
top_top_o: $o ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
top_top_set_state_o2: set_state_o ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
top_top_set_state: set_state ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
top_to5262587396890829782_state: set_set_state ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J_J,type,
top_to3598970937283095436_state: set_set_set_state ).
thf(sy_c_Set_OCollect_001t__PartialHeapSA__Ostate,type,
collect_state: ( state > $o ) > set_state ).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
collect_set_state: ( set_state > $o ) > set_set_state ).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
collec1217220441665645051_state: ( set_set_state > $o ) > set_set_set_state ).
thf(sy_c_Set_OPow_001t__PartialHeapSA__Ostate,type,
pow_state: set_state > set_set_state ).
thf(sy_c_Set_Oimage_001t__PartialHeapSA__Ostate_001t__PartialHeapSA__Ostate,type,
image_state_state: ( state > state ) > set_state > set_state ).
thf(sy_c_Set_Oimage_001t__PartialHeapSA__Ostate_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
image_4774290769506072625_state: ( state > set_state ) > set_state > set_set_state ).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__PartialHeapSA__Ostate_J_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
image_2476256681063834599_state: ( set_state > set_state ) > set_set_state > set_set_state ).
thf(sy_c_Set_Oinsert_001t__PartialHeapSA__Ostate,type,
insert_state: state > set_state > set_state ).
thf(sy_c_Set_Oinsert_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
insert_set_state: set_state > set_set_state > set_set_state ).
thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
insert_set_set_state: set_set_state > set_set_set_state > set_set_set_state ).
thf(sy_c_Set_Ois__empty_001t__PartialHeapSA__Ostate,type,
is_empty_state: set_state > $o ).
thf(sy_c_Set_Ois__empty_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
is_empty_set_state: set_set_state > $o ).
thf(sy_c_Set_Ois__singleton_001t__PartialHeapSA__Ostate,type,
is_singleton_state: set_state > $o ).
thf(sy_c_Set_Ois__singleton_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
is_sin3747817797122030204_state: set_set_state > $o ).
thf(sy_c_Set_Ois__singleton_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
is_sin6783755808700971314_state: set_set_set_state > $o ).
thf(sy_c_Set_Opairwise_001t__PartialHeapSA__Ostate,type,
pairwise_state: ( state > state > $o ) > set_state > $o ).
thf(sy_c_Set_Opairwise_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
pairwise_set_state: ( set_state > set_state > $o ) > set_set_state > $o ).
thf(sy_c_Set_Opairwise_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
pairwi6477347089298328827_state: ( set_set_state > set_set_state > $o ) > set_set_set_state > $o ).
thf(sy_c_Set_Oremove_001t__PartialHeapSA__Ostate,type,
remove_state: state > set_state > set_state ).
thf(sy_c_Set_Othe__elem_001t__PartialHeapSA__Ostate,type,
the_elem_state: set_state > state ).
thf(sy_c_Set_Othe__elem_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
the_elem_set_state: set_set_state > set_state ).
thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or7399831441507084590_state: ( $o > set_state ) > ( $o > set_state ) > set_o_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
set_or2467210022473197514tate_o: ( state > $o ) > ( state > $o ) > set_state_o ).
thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
set_or701696889746204795_state: set_state > set_state > set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or7796883608616495921_state: set_set_state > set_set_state > set_set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or8134177505681183498_state: ( $o > set_state ) > ( $o > set_state ) > set_o_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
set_or2838015025653527455_state: set_state > set_state > set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or5996981303281673813_state: set_set_state > set_set_state > set_set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatLeast_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or8064825548156300868_state: ( $o > set_state ) > set_o_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
set_or6477372120337742821_state: set_state > set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or922425460254742171_state: set_set_state > set_set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatMost_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or7255946770513471040_state: ( $o > set_state ) > set_o_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatMost_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
set_or1722117244622138588tate_o: ( state > $o ) > set_state_o ).
thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
set_or5536065684288934121_state: set_state > set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or8190520063335472031_state: set_set_state > set_set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or9083347566284363977_state: ( $o > set_state ) > ( $o > set_state ) > set_o_set_state ).
thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
set_or5184245929044373792_state: set_state > set_state > set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or8261726110466482134_state: set_set_state > set_set_state > set_set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or9151442426322445605_state: ( $o > set_state ) > ( $o > set_state ) > set_o_set_state ).
thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
set_or421293776985356740_state: set_state > set_state > set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or4346910941253671034_state: set_set_state > set_set_state > set_set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
set_or7996350251103833098_state: set_state > set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or8484835426764182208_state: set_set_state > set_set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OlessThan_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
set_or3075120673672437176tate_o: ( state > $o ) > set_state_o ).
thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
set_or1034127368735114509_state: set_state > set_set_state ).
thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
set_or5856722414167211971_state: set_set_state > set_set_set_state ).
thf(sy_c_Zorn_Ochains_001t__PartialHeapSA__Ostate,type,
chains_state: set_set_state > set_set_set_state ).
thf(sy_c_Zorn_Opred__on_Ochain_001t__PartialHeapSA__Ostate,type,
pred_chain_state: set_state > ( state > state > $o ) > set_state > $o ).
thf(sy_c_Zorn_Opred__on_Ochain_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
pred_chain_set_state: set_set_state > ( set_state > set_state > $o ) > set_set_state > $o ).
thf(sy_c_member_001_062_I_Eo_Mt__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
member_o_set_state: ( $o > set_state ) > set_o_set_state > $o ).
thf(sy_c_member_001_062_It__PartialHeapSA__Ostate_M_062_It__PartialHeapSA__Ostate_M_Eo_J_J,type,
member_state_state_o: ( state > state > $o ) > set_state_state_o > $o ).
thf(sy_c_member_001_062_It__PartialHeapSA__Ostate_M_Eo_J,type,
member_state_o: ( state > $o ) > set_state_o > $o ).
thf(sy_c_member_001t__PartialHeapSA__Ostate,type,
member_state: state > set_state > $o ).
thf(sy_c_member_001t__Set__Oset_It__PartialHeapSA__Ostate_J,type,
member_set_state: set_state > set_set_state > $o ).
thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__PartialHeapSA__Ostate_J_J,type,
member_set_set_state: set_set_state > set_set_set_state > $o ).
thf(sy_v_A,type,
a: set_state ).
thf(sy_v_B,type,
b: set_state ).
% Relevant facts (1276)
thf(fact_0_subsetI,axiom,
! [A: set_set_set_state,B: set_set_set_state] :
( ! [X: set_set_state] :
( ( member_set_set_state @ X @ A )
=> ( member_set_set_state @ X @ B ) )
=> ( ord_le3154822624800881980_state @ A @ B ) ) ).
% subsetI
thf(fact_1_subsetI,axiom,
! [A: set_set_state,B: set_set_state] :
( ! [X: set_state] :
( ( member_set_state @ X @ A )
=> ( member_set_state @ X @ B ) )
=> ( ord_le5175021213330142598_state @ A @ B ) ) ).
% subsetI
thf(fact_2_subsetI,axiom,
! [A: set_state,B: set_state] :
( ! [X: state] :
( ( member_state @ X @ A )
=> ( member_state @ X @ B ) )
=> ( ord_le2494988322063910608_state @ A @ B ) ) ).
% subsetI
thf(fact_3_double__inclusion,axiom,
! [A: set_set_state,B: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ B )
=> ( ( ord_le5175021213330142598_state @ B @ A )
=> ( A = B ) ) ) ).
% double_inclusion
thf(fact_4_double__inclusion,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( ord_le2494988322063910608_state @ B @ A )
=> ( A = B ) ) ) ).
% double_inclusion
thf(fact_5_order__refl,axiom,
! [X2: $o > set_state] : ( ord_le9189382018855386905_state @ X2 @ X2 ) ).
% order_refl
thf(fact_6_order__refl,axiom,
! [X2: set_set_state] : ( ord_le5175021213330142598_state @ X2 @ X2 ) ).
% order_refl
thf(fact_7_order__refl,axiom,
! [X2: set_state] : ( ord_le2494988322063910608_state @ X2 @ X2 ) ).
% order_refl
thf(fact_8_dual__order_Orefl,axiom,
! [A2: $o > set_state] : ( ord_le9189382018855386905_state @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_9_dual__order_Orefl,axiom,
! [A2: set_set_state] : ( ord_le5175021213330142598_state @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_10_dual__order_Orefl,axiom,
! [A2: set_state] : ( ord_le2494988322063910608_state @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_11_in__mono,axiom,
! [A: set_set_set_state,B: set_set_set_state,X2: set_set_state] :
( ( ord_le3154822624800881980_state @ A @ B )
=> ( ( member_set_set_state @ X2 @ A )
=> ( member_set_set_state @ X2 @ B ) ) ) ).
% in_mono
thf(fact_12_in__mono,axiom,
! [A: set_set_state,B: set_set_state,X2: set_state] :
( ( ord_le5175021213330142598_state @ A @ B )
=> ( ( member_set_state @ X2 @ A )
=> ( member_set_state @ X2 @ B ) ) ) ).
% in_mono
thf(fact_13_in__mono,axiom,
! [A: set_state,B: set_state,X2: state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( member_state @ X2 @ A )
=> ( member_state @ X2 @ B ) ) ) ).
% in_mono
thf(fact_14_subsetD,axiom,
! [A: set_set_set_state,B: set_set_set_state,C: set_set_state] :
( ( ord_le3154822624800881980_state @ A @ B )
=> ( ( member_set_set_state @ C @ A )
=> ( member_set_set_state @ C @ B ) ) ) ).
% subsetD
thf(fact_15_subsetD,axiom,
! [A: set_set_state,B: set_set_state,C: set_state] :
( ( ord_le5175021213330142598_state @ A @ B )
=> ( ( member_set_state @ C @ A )
=> ( member_set_state @ C @ B ) ) ) ).
% subsetD
thf(fact_16_subsetD,axiom,
! [A: set_state,B: set_state,C: state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( member_state @ C @ A )
=> ( member_state @ C @ B ) ) ) ).
% subsetD
thf(fact_17_equalityE,axiom,
! [A: set_set_state,B: set_set_state] :
( ( A = B )
=> ~ ( ( ord_le5175021213330142598_state @ A @ B )
=> ~ ( ord_le5175021213330142598_state @ B @ A ) ) ) ).
% equalityE
thf(fact_18_equalityE,axiom,
! [A: set_state,B: set_state] :
( ( A = B )
=> ~ ( ( ord_le2494988322063910608_state @ A @ B )
=> ~ ( ord_le2494988322063910608_state @ B @ A ) ) ) ).
% equalityE
thf(fact_19_subset__eq,axiom,
( ord_le3154822624800881980_state
= ( ^ [A3: set_set_set_state,B2: set_set_set_state] :
! [X3: set_set_state] :
( ( member_set_set_state @ X3 @ A3 )
=> ( member_set_set_state @ X3 @ B2 ) ) ) ) ).
% subset_eq
thf(fact_20_subset__eq,axiom,
( ord_le5175021213330142598_state
= ( ^ [A3: set_set_state,B2: set_set_state] :
! [X3: set_state] :
( ( member_set_state @ X3 @ A3 )
=> ( member_set_state @ X3 @ B2 ) ) ) ) ).
% subset_eq
thf(fact_21_subset__eq,axiom,
( ord_le2494988322063910608_state
= ( ^ [A3: set_state,B2: set_state] :
! [X3: state] :
( ( member_state @ X3 @ A3 )
=> ( member_state @ X3 @ B2 ) ) ) ) ).
% subset_eq
thf(fact_22_equalityD1,axiom,
! [A: set_set_state,B: set_set_state] :
( ( A = B )
=> ( ord_le5175021213330142598_state @ A @ B ) ) ).
% equalityD1
thf(fact_23_equalityD1,axiom,
! [A: set_state,B: set_state] :
( ( A = B )
=> ( ord_le2494988322063910608_state @ A @ B ) ) ).
% equalityD1
thf(fact_24_equalityD2,axiom,
! [A: set_set_state,B: set_set_state] :
( ( A = B )
=> ( ord_le5175021213330142598_state @ B @ A ) ) ).
% equalityD2
thf(fact_25_equalityD2,axiom,
! [A: set_state,B: set_state] :
( ( A = B )
=> ( ord_le2494988322063910608_state @ B @ A ) ) ).
% equalityD2
thf(fact_26_subset__iff,axiom,
( ord_le3154822624800881980_state
= ( ^ [A3: set_set_set_state,B2: set_set_set_state] :
! [T: set_set_state] :
( ( member_set_set_state @ T @ A3 )
=> ( member_set_set_state @ T @ B2 ) ) ) ) ).
% subset_iff
thf(fact_27_subset__iff,axiom,
( ord_le5175021213330142598_state
= ( ^ [A3: set_set_state,B2: set_set_state] :
! [T: set_state] :
( ( member_set_state @ T @ A3 )
=> ( member_set_state @ T @ B2 ) ) ) ) ).
% subset_iff
thf(fact_28_subset__iff,axiom,
( ord_le2494988322063910608_state
= ( ^ [A3: set_state,B2: set_state] :
! [T: state] :
( ( member_state @ T @ A3 )
=> ( member_state @ T @ B2 ) ) ) ) ).
% subset_iff
thf(fact_29_subset__refl,axiom,
! [A: set_set_state] : ( ord_le5175021213330142598_state @ A @ A ) ).
% subset_refl
thf(fact_30_subset__refl,axiom,
! [A: set_state] : ( ord_le2494988322063910608_state @ A @ A ) ).
% subset_refl
thf(fact_31_order__antisym__conv,axiom,
! [Y: $o > set_state,X2: $o > set_state] :
( ( ord_le9189382018855386905_state @ Y @ X2 )
=> ( ( ord_le9189382018855386905_state @ X2 @ Y )
= ( X2 = Y ) ) ) ).
% order_antisym_conv
thf(fact_32_order__antisym__conv,axiom,
! [Y: set_set_state,X2: set_set_state] :
( ( ord_le5175021213330142598_state @ Y @ X2 )
=> ( ( ord_le5175021213330142598_state @ X2 @ Y )
= ( X2 = Y ) ) ) ).
% order_antisym_conv
thf(fact_33_order__antisym__conv,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_le2494988322063910608_state @ Y @ X2 )
=> ( ( ord_le2494988322063910608_state @ X2 @ Y )
= ( X2 = Y ) ) ) ).
% order_antisym_conv
thf(fact_34_ord__le__eq__subst,axiom,
! [A2: set_state,B3: set_state,F: set_state > $o > set_state,C: $o > set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_35_ord__le__eq__subst,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_set_state,C: set_set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_36_ord__le__eq__subst,axiom,
! [A2: $o > set_state,B3: $o > set_state,F: ( $o > set_state ) > set_state,C: set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_37_ord__le__eq__subst,axiom,
! [A2: $o > set_state,B3: $o > set_state,F: ( $o > set_state ) > $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_38_ord__le__eq__subst,axiom,
! [A2: $o > set_state,B3: $o > set_state,F: ( $o > set_state ) > set_set_state,C: set_set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_39_ord__le__eq__subst,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_state,C: set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_40_ord__le__eq__subst,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > $o > set_state,C: $o > set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_41_ord__le__eq__subst,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_42_ord__le__eq__subst,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_43_ord__eq__le__subst,axiom,
! [A2: $o > set_state,F: set_state > $o > set_state,B3: set_state,C: set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_44_ord__eq__le__subst,axiom,
! [A2: set_set_state,F: set_state > set_set_state,B3: set_state,C: set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_45_ord__eq__le__subst,axiom,
! [A2: set_state,F: ( $o > set_state ) > set_state,B3: $o > set_state,C: $o > set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_46_ord__eq__le__subst,axiom,
! [A2: $o > set_state,F: ( $o > set_state ) > $o > set_state,B3: $o > set_state,C: $o > set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_47_ord__eq__le__subst,axiom,
! [A2: set_set_state,F: ( $o > set_state ) > set_set_state,B3: $o > set_state,C: $o > set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_48_ord__eq__le__subst,axiom,
! [A2: set_state,F: set_set_state > set_state,B3: set_set_state,C: set_set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_49_ord__eq__le__subst,axiom,
! [A2: $o > set_state,F: set_set_state > $o > set_state,B3: set_set_state,C: set_set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_50_ord__eq__le__subst,axiom,
! [A2: set_set_state,F: set_set_state > set_set_state,B3: set_set_state,C: set_set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_51_ord__eq__le__subst,axiom,
! [A2: set_state,F: set_state > set_state,B3: set_state,C: set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_52_order__eq__refl,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( X2 = Y )
=> ( ord_le9189382018855386905_state @ X2 @ Y ) ) ).
% order_eq_refl
thf(fact_53_order__eq__refl,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( X2 = Y )
=> ( ord_le5175021213330142598_state @ X2 @ Y ) ) ).
% order_eq_refl
thf(fact_54_order__eq__refl,axiom,
! [X2: set_state,Y: set_state] :
( ( X2 = Y )
=> ( ord_le2494988322063910608_state @ X2 @ Y ) ) ).
% order_eq_refl
thf(fact_55_order__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > $o > set_state,C: $o > set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_le9189382018855386905_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_56_order__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_set_state,C: set_set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_le5175021213330142598_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_57_order__subst2,axiom,
! [A2: $o > set_state,B3: $o > set_state,F: ( $o > set_state ) > set_state,C: set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ ( F @ B3 ) @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_58_order__subst2,axiom,
! [A2: $o > set_state,B3: $o > set_state,F: ( $o > set_state ) > $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_le9189382018855386905_state @ ( F @ B3 ) @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_59_order__subst2,axiom,
! [A2: $o > set_state,B3: $o > set_state,F: ( $o > set_state ) > set_set_state,C: set_set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_le5175021213330142598_state @ ( F @ B3 ) @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_60_order__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_state,C: set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_61_order__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > $o > set_state,C: $o > set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_le9189382018855386905_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_62_order__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_le5175021213330142598_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_63_order__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_64_order__subst1,axiom,
! [A2: set_state,F: ( $o > set_state ) > set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_le2494988322063910608_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_65_order__subst1,axiom,
! [A2: set_state,F: set_set_state > set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le2494988322063910608_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_66_order__subst1,axiom,
! [A2: $o > set_state,F: set_state > $o > set_state,B3: set_state,C: set_state] :
( ( ord_le9189382018855386905_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_67_order__subst1,axiom,
! [A2: $o > set_state,F: ( $o > set_state ) > $o > set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_68_order__subst1,axiom,
! [A2: $o > set_state,F: set_set_state > $o > set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le9189382018855386905_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le9189382018855386905_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_69_order__subst1,axiom,
! [A2: set_set_state,F: set_state > set_set_state,B3: set_state,C: set_state] :
( ( ord_le5175021213330142598_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_70_order__subst1,axiom,
! [A2: set_set_state,F: ( $o > set_state ) > set_set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_le5175021213330142598_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_71_order__subst1,axiom,
! [A2: set_set_state,F: set_set_state > set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le5175021213330142598_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_72_order__subst1,axiom,
! [A2: set_state,F: set_state > set_state,B3: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le2494988322063910608_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_73_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y3: $o > set_state,Z: $o > set_state] : ( Y3 = Z ) )
= ( ^ [A4: $o > set_state,B4: $o > set_state] :
( ( ord_le9189382018855386905_state @ A4 @ B4 )
& ( ord_le9189382018855386905_state @ B4 @ A4 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_74_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y3: set_set_state,Z: set_set_state] : ( Y3 = Z ) )
= ( ^ [A4: set_set_state,B4: set_set_state] :
( ( ord_le5175021213330142598_state @ A4 @ B4 )
& ( ord_le5175021213330142598_state @ B4 @ A4 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_75_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y3: set_state,Z: set_state] : ( Y3 = Z ) )
= ( ^ [A4: set_state,B4: set_state] :
( ( ord_le2494988322063910608_state @ A4 @ B4 )
& ( ord_le2494988322063910608_state @ B4 @ A4 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_76_le__fun__def,axiom,
( ord_le9189382018855386905_state
= ( ^ [F2: $o > set_state,G: $o > set_state] :
! [X3: $o] : ( ord_le2494988322063910608_state @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% le_fun_def
thf(fact_77_le__funI,axiom,
! [F: $o > set_state,G2: $o > set_state] :
( ! [X: $o] : ( ord_le2494988322063910608_state @ ( F @ X ) @ ( G2 @ X ) )
=> ( ord_le9189382018855386905_state @ F @ G2 ) ) ).
% le_funI
thf(fact_78_le__funE,axiom,
! [F: $o > set_state,G2: $o > set_state,X2: $o] :
( ( ord_le9189382018855386905_state @ F @ G2 )
=> ( ord_le2494988322063910608_state @ ( F @ X2 ) @ ( G2 @ X2 ) ) ) ).
% le_funE
thf(fact_79_le__funD,axiom,
! [F: $o > set_state,G2: $o > set_state,X2: $o] :
( ( ord_le9189382018855386905_state @ F @ G2 )
=> ( ord_le2494988322063910608_state @ ( F @ X2 ) @ ( G2 @ X2 ) ) ) ).
% le_funD
thf(fact_80_antisym,axiom,
! [A2: $o > set_state,B3: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_le9189382018855386905_state @ B3 @ A2 )
=> ( A2 = B3 ) ) ) ).
% antisym
thf(fact_81_antisym,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_le5175021213330142598_state @ B3 @ A2 )
=> ( A2 = B3 ) ) ) ).
% antisym
thf(fact_82_antisym,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ( A2 = B3 ) ) ) ).
% antisym
thf(fact_83_dual__order_Otrans,axiom,
! [B3: $o > set_state,A2: $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ B3 @ A2 )
=> ( ( ord_le9189382018855386905_state @ C @ B3 )
=> ( ord_le9189382018855386905_state @ C @ A2 ) ) ) ).
% dual_order.trans
thf(fact_84_dual__order_Otrans,axiom,
! [B3: set_set_state,A2: set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ B3 @ A2 )
=> ( ( ord_le5175021213330142598_state @ C @ B3 )
=> ( ord_le5175021213330142598_state @ C @ A2 ) ) ) ).
% dual_order.trans
thf(fact_85_dual__order_Otrans,axiom,
! [B3: set_state,A2: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ( ( ord_le2494988322063910608_state @ C @ B3 )
=> ( ord_le2494988322063910608_state @ C @ A2 ) ) ) ).
% dual_order.trans
thf(fact_86_dual__order_Oantisym,axiom,
! [B3: $o > set_state,A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ B3 @ A2 )
=> ( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( A2 = B3 ) ) ) ).
% dual_order.antisym
thf(fact_87_dual__order_Oantisym,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( ord_le5175021213330142598_state @ B3 @ A2 )
=> ( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( A2 = B3 ) ) ) ).
% dual_order.antisym
thf(fact_88_dual__order_Oantisym,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( A2 = B3 ) ) ) ).
% dual_order.antisym
thf(fact_89_dual__order_Oeq__iff,axiom,
( ( ^ [Y3: $o > set_state,Z: $o > set_state] : ( Y3 = Z ) )
= ( ^ [A4: $o > set_state,B4: $o > set_state] :
( ( ord_le9189382018855386905_state @ B4 @ A4 )
& ( ord_le9189382018855386905_state @ A4 @ B4 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_90_dual__order_Oeq__iff,axiom,
( ( ^ [Y3: set_set_state,Z: set_set_state] : ( Y3 = Z ) )
= ( ^ [A4: set_set_state,B4: set_set_state] :
( ( ord_le5175021213330142598_state @ B4 @ A4 )
& ( ord_le5175021213330142598_state @ A4 @ B4 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_91_dual__order_Oeq__iff,axiom,
( ( ^ [Y3: set_state,Z: set_state] : ( Y3 = Z ) )
= ( ^ [A4: set_state,B4: set_state] :
( ( ord_le2494988322063910608_state @ B4 @ A4 )
& ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_92_order__trans,axiom,
! [X2: $o > set_state,Y: $o > set_state,Z2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ Y )
=> ( ( ord_le9189382018855386905_state @ Y @ Z2 )
=> ( ord_le9189382018855386905_state @ X2 @ Z2 ) ) ) ).
% order_trans
thf(fact_93_order__trans,axiom,
! [X2: set_set_state,Y: set_set_state,Z2: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ Y )
=> ( ( ord_le5175021213330142598_state @ Y @ Z2 )
=> ( ord_le5175021213330142598_state @ X2 @ Z2 ) ) ) ).
% order_trans
thf(fact_94_order__trans,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( ord_le2494988322063910608_state @ Y @ Z2 )
=> ( ord_le2494988322063910608_state @ X2 @ Z2 ) ) ) ).
% order_trans
thf(fact_95_order_Otrans,axiom,
! [A2: $o > set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ord_le9189382018855386905_state @ A2 @ C ) ) ) ).
% order.trans
thf(fact_96_order_Otrans,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ord_le5175021213330142598_state @ A2 @ C ) ) ) ).
% order.trans
thf(fact_97_order_Otrans,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ord_le2494988322063910608_state @ A2 @ C ) ) ) ).
% order.trans
thf(fact_98_order__antisym,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ Y )
=> ( ( ord_le9189382018855386905_state @ Y @ X2 )
=> ( X2 = Y ) ) ) ).
% order_antisym
thf(fact_99_order__antisym,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ Y )
=> ( ( ord_le5175021213330142598_state @ Y @ X2 )
=> ( X2 = Y ) ) ) ).
% order_antisym
thf(fact_100_order__antisym,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( ord_le2494988322063910608_state @ Y @ X2 )
=> ( X2 = Y ) ) ) ).
% order_antisym
thf(fact_101_ord__le__eq__trans,axiom,
! [A2: $o > set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( B3 = C )
=> ( ord_le9189382018855386905_state @ A2 @ C ) ) ) ).
% ord_le_eq_trans
thf(fact_102_ord__le__eq__trans,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( B3 = C )
=> ( ord_le5175021213330142598_state @ A2 @ C ) ) ) ).
% ord_le_eq_trans
thf(fact_103_ord__le__eq__trans,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( B3 = C )
=> ( ord_le2494988322063910608_state @ A2 @ C ) ) ) ).
% ord_le_eq_trans
thf(fact_104_ord__eq__le__trans,axiom,
! [A2: $o > set_state,B3: $o > set_state,C: $o > set_state] :
( ( A2 = B3 )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ord_le9189382018855386905_state @ A2 @ C ) ) ) ).
% ord_eq_le_trans
thf(fact_105_ord__eq__le__trans,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state] :
( ( A2 = B3 )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ord_le5175021213330142598_state @ A2 @ C ) ) ) ).
% ord_eq_le_trans
thf(fact_106_ord__eq__le__trans,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( A2 = B3 )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ord_le2494988322063910608_state @ A2 @ C ) ) ) ).
% ord_eq_le_trans
thf(fact_107_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y3: $o > set_state,Z: $o > set_state] : ( Y3 = Z ) )
= ( ^ [X3: $o > set_state,Y4: $o > set_state] :
( ( ord_le9189382018855386905_state @ X3 @ Y4 )
& ( ord_le9189382018855386905_state @ Y4 @ X3 ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_108_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y3: set_set_state,Z: set_set_state] : ( Y3 = Z ) )
= ( ^ [X3: set_set_state,Y4: set_set_state] :
( ( ord_le5175021213330142598_state @ X3 @ Y4 )
& ( ord_le5175021213330142598_state @ Y4 @ X3 ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_109_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y3: set_state,Z: set_state] : ( Y3 = Z ) )
= ( ^ [X3: set_state,Y4: set_state] :
( ( ord_le2494988322063910608_state @ X3 @ Y4 )
& ( ord_le2494988322063910608_state @ Y4 @ X3 ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_110_Collect__mono__iff,axiom,
! [P: set_state > $o,Q: set_state > $o] :
( ( ord_le5175021213330142598_state @ ( collect_set_state @ P ) @ ( collect_set_state @ Q ) )
= ( ! [X3: set_state] :
( ( P @ X3 )
=> ( Q @ X3 ) ) ) ) ).
% Collect_mono_iff
thf(fact_111_Collect__mono__iff,axiom,
! [P: state > $o,Q: state > $o] :
( ( ord_le2494988322063910608_state @ ( collect_state @ P ) @ ( collect_state @ Q ) )
= ( ! [X3: state] :
( ( P @ X3 )
=> ( Q @ X3 ) ) ) ) ).
% Collect_mono_iff
thf(fact_112_set__eq__subset,axiom,
( ( ^ [Y3: set_set_state,Z: set_set_state] : ( Y3 = Z ) )
= ( ^ [A3: set_set_state,B2: set_set_state] :
( ( ord_le5175021213330142598_state @ A3 @ B2 )
& ( ord_le5175021213330142598_state @ B2 @ A3 ) ) ) ) ).
% set_eq_subset
thf(fact_113_set__eq__subset,axiom,
( ( ^ [Y3: set_state,Z: set_state] : ( Y3 = Z ) )
= ( ^ [A3: set_state,B2: set_state] :
( ( ord_le2494988322063910608_state @ A3 @ B2 )
& ( ord_le2494988322063910608_state @ B2 @ A3 ) ) ) ) ).
% set_eq_subset
thf(fact_114_subset__trans,axiom,
! [A: set_set_state,B: set_set_state,C2: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ B )
=> ( ( ord_le5175021213330142598_state @ B @ C2 )
=> ( ord_le5175021213330142598_state @ A @ C2 ) ) ) ).
% subset_trans
thf(fact_115_subset__trans,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( ord_le2494988322063910608_state @ B @ C2 )
=> ( ord_le2494988322063910608_state @ A @ C2 ) ) ) ).
% subset_trans
thf(fact_116_Collect__mono,axiom,
! [P: set_state > $o,Q: set_state > $o] :
( ! [X: set_state] :
( ( P @ X )
=> ( Q @ X ) )
=> ( ord_le5175021213330142598_state @ ( collect_set_state @ P ) @ ( collect_set_state @ Q ) ) ) ).
% Collect_mono
thf(fact_117_Collect__mono,axiom,
! [P: state > $o,Q: state > $o] :
( ! [X: state] :
( ( P @ X )
=> ( Q @ X ) )
=> ( ord_le2494988322063910608_state @ ( collect_state @ P ) @ ( collect_state @ Q ) ) ) ).
% Collect_mono
thf(fact_118_Greatest__equality,axiom,
! [P: ( $o > set_state ) > $o,X2: $o > set_state] :
( ( P @ X2 )
=> ( ! [Y2: $o > set_state] :
( ( P @ Y2 )
=> ( ord_le9189382018855386905_state @ Y2 @ X2 ) )
=> ( ( order_1484864080787882322_state @ P )
= X2 ) ) ) ).
% Greatest_equality
thf(fact_119_Greatest__equality,axiom,
! [P: set_set_state > $o,X2: set_set_state] :
( ( P @ X2 )
=> ( ! [Y2: set_set_state] :
( ( P @ Y2 )
=> ( ord_le5175021213330142598_state @ Y2 @ X2 ) )
=> ( ( order_6508859784380345869_state @ P )
= X2 ) ) ) ).
% Greatest_equality
thf(fact_120_Greatest__equality,axiom,
! [P: set_state > $o,X2: set_state] :
( ( P @ X2 )
=> ( ! [Y2: set_state] :
( ( P @ Y2 )
=> ( ord_le2494988322063910608_state @ Y2 @ X2 ) )
=> ( ( order_2642746146112740183_state @ P )
= X2 ) ) ) ).
% Greatest_equality
thf(fact_121_GreatestI2__order,axiom,
! [P: ( $o > set_state ) > $o,X2: $o > set_state,Q: ( $o > set_state ) > $o] :
( ( P @ X2 )
=> ( ! [Y2: $o > set_state] :
( ( P @ Y2 )
=> ( ord_le9189382018855386905_state @ Y2 @ X2 ) )
=> ( ! [X: $o > set_state] :
( ( P @ X )
=> ( ! [Y5: $o > set_state] :
( ( P @ Y5 )
=> ( ord_le9189382018855386905_state @ Y5 @ X ) )
=> ( Q @ X ) ) )
=> ( Q @ ( order_1484864080787882322_state @ P ) ) ) ) ) ).
% GreatestI2_order
thf(fact_122_GreatestI2__order,axiom,
! [P: set_set_state > $o,X2: set_set_state,Q: set_set_state > $o] :
( ( P @ X2 )
=> ( ! [Y2: set_set_state] :
( ( P @ Y2 )
=> ( ord_le5175021213330142598_state @ Y2 @ X2 ) )
=> ( ! [X: set_set_state] :
( ( P @ X )
=> ( ! [Y5: set_set_state] :
( ( P @ Y5 )
=> ( ord_le5175021213330142598_state @ Y5 @ X ) )
=> ( Q @ X ) ) )
=> ( Q @ ( order_6508859784380345869_state @ P ) ) ) ) ) ).
% GreatestI2_order
thf(fact_123_GreatestI2__order,axiom,
! [P: set_state > $o,X2: set_state,Q: set_state > $o] :
( ( P @ X2 )
=> ( ! [Y2: set_state] :
( ( P @ Y2 )
=> ( ord_le2494988322063910608_state @ Y2 @ X2 ) )
=> ( ! [X: set_state] :
( ( P @ X )
=> ( ! [Y5: set_state] :
( ( P @ Y5 )
=> ( ord_le2494988322063910608_state @ Y5 @ X ) )
=> ( Q @ X ) ) )
=> ( Q @ ( order_2642746146112740183_state @ P ) ) ) ) ) ).
% GreatestI2_order
thf(fact_124_le__rel__bool__arg__iff,axiom,
( ord_le621814680099590950_state
= ( ^ [X4: $o > $o > set_state,Y6: $o > $o > set_state] :
( ( ord_le9189382018855386905_state @ ( X4 @ $false ) @ ( Y6 @ $false ) )
& ( ord_le9189382018855386905_state @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% le_rel_bool_arg_iff
thf(fact_125_le__rel__bool__arg__iff,axiom,
( ord_le6992062077777787599_state
= ( ^ [X4: $o > set_set_state,Y6: $o > set_set_state] :
( ( ord_le5175021213330142598_state @ ( X4 @ $false ) @ ( Y6 @ $false ) )
& ( ord_le5175021213330142598_state @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% le_rel_bool_arg_iff
thf(fact_126_le__rel__bool__arg__iff,axiom,
( ord_le9189382018855386905_state
= ( ^ [X4: $o > set_state,Y6: $o > set_state] :
( ( ord_le2494988322063910608_state @ ( X4 @ $false ) @ ( Y6 @ $false ) )
& ( ord_le2494988322063910608_state @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% le_rel_bool_arg_iff
thf(fact_127_mem__Collect__eq,axiom,
! [A2: set_state,P: set_state > $o] :
( ( member_set_state @ A2 @ ( collect_set_state @ P ) )
= ( P @ A2 ) ) ).
% mem_Collect_eq
thf(fact_128_mem__Collect__eq,axiom,
! [A2: set_set_state,P: set_set_state > $o] :
( ( member_set_set_state @ A2 @ ( collec1217220441665645051_state @ P ) )
= ( P @ A2 ) ) ).
% mem_Collect_eq
thf(fact_129_mem__Collect__eq,axiom,
! [A2: state,P: state > $o] :
( ( member_state @ A2 @ ( collect_state @ P ) )
= ( P @ A2 ) ) ).
% mem_Collect_eq
thf(fact_130_Collect__mem__eq,axiom,
! [A: set_set_state] :
( ( collect_set_state
@ ^ [X3: set_state] : ( member_set_state @ X3 @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_131_Collect__mem__eq,axiom,
! [A: set_set_set_state] :
( ( collec1217220441665645051_state
@ ^ [X3: set_set_state] : ( member_set_set_state @ X3 @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_132_Collect__mem__eq,axiom,
! [A: set_state] :
( ( collect_state
@ ^ [X3: state] : ( member_state @ X3 @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_133_Collect__cong,axiom,
! [P: state > $o,Q: state > $o] :
( ! [X: state] :
( ( P @ X )
= ( Q @ X ) )
=> ( ( collect_state @ P )
= ( collect_state @ Q ) ) ) ).
% Collect_cong
thf(fact_134_verit__comp__simplify1_I2_J,axiom,
! [A2: $o > set_state] : ( ord_le9189382018855386905_state @ A2 @ A2 ) ).
% verit_comp_simplify1(2)
thf(fact_135_verit__comp__simplify1_I2_J,axiom,
! [A2: set_set_state] : ( ord_le5175021213330142598_state @ A2 @ A2 ) ).
% verit_comp_simplify1(2)
thf(fact_136_verit__comp__simplify1_I2_J,axiom,
! [A2: set_state] : ( ord_le2494988322063910608_state @ A2 @ A2 ) ).
% verit_comp_simplify1(2)
thf(fact_137_order_Opartial__preordering__axioms,axiom,
partia1090249825177899695_state @ ord_le9189382018855386905_state ).
% order.partial_preordering_axioms
thf(fact_138_order_Opartial__preordering__axioms,axiom,
partia4579038784995701360_state @ ord_le5175021213330142598_state ).
% order.partial_preordering_axioms
thf(fact_139_order_Opartial__preordering__axioms,axiom,
partia7871104319988624314_state @ ord_le2494988322063910608_state ).
% order.partial_preordering_axioms
thf(fact_140_atLeast__subset__iff,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_le4652835513209282297_state @ ( set_or8064825548156300868_state @ X2 ) @ ( set_or8064825548156300868_state @ Y ) )
= ( ord_le9189382018855386905_state @ Y @ X2 ) ) ).
% atLeast_subset_iff
thf(fact_141_atLeast__subset__iff,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le3154822624800881980_state @ ( set_or922425460254742171_state @ X2 ) @ ( set_or922425460254742171_state @ Y ) )
= ( ord_le5175021213330142598_state @ Y @ X2 ) ) ).
% atLeast_subset_iff
thf(fact_142_atLeast__subset__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le5175021213330142598_state @ ( set_or6477372120337742821_state @ X2 ) @ ( set_or6477372120337742821_state @ Y ) )
= ( ord_le2494988322063910608_state @ Y @ X2 ) ) ).
% atLeast_subset_iff
thf(fact_143_atMost__subset__iff,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_le4652835513209282297_state @ ( set_or7255946770513471040_state @ X2 ) @ ( set_or7255946770513471040_state @ Y ) )
= ( ord_le9189382018855386905_state @ X2 @ Y ) ) ).
% atMost_subset_iff
thf(fact_144_atMost__subset__iff,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le3154822624800881980_state @ ( set_or8190520063335472031_state @ X2 ) @ ( set_or8190520063335472031_state @ Y ) )
= ( ord_le5175021213330142598_state @ X2 @ Y ) ) ).
% atMost_subset_iff
thf(fact_145_atMost__subset__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le5175021213330142598_state @ ( set_or5536065684288934121_state @ X2 ) @ ( set_or5536065684288934121_state @ Y ) )
= ( ord_le2494988322063910608_state @ X2 @ Y ) ) ).
% atMost_subset_iff
thf(fact_146_pairwise__subset,axiom,
! [P: set_state > set_state > $o,S: set_set_state,T2: set_set_state] :
( ( pairwise_set_state @ P @ S )
=> ( ( ord_le5175021213330142598_state @ T2 @ S )
=> ( pairwise_set_state @ P @ T2 ) ) ) ).
% pairwise_subset
thf(fact_147_pairwise__subset,axiom,
! [P: state > state > $o,S: set_state,T2: set_state] :
( ( pairwise_state @ P @ S )
=> ( ( ord_le2494988322063910608_state @ T2 @ S )
=> ( pairwise_state @ P @ T2 ) ) ) ).
% pairwise_subset
thf(fact_148_pairwise__mono,axiom,
! [P: set_state > set_state > $o,A: set_set_state,Q: set_state > set_state > $o,B: set_set_state] :
( ( pairwise_set_state @ P @ A )
=> ( ! [X: set_state,Y2: set_state] :
( ( P @ X @ Y2 )
=> ( Q @ X @ Y2 ) )
=> ( ( ord_le5175021213330142598_state @ B @ A )
=> ( pairwise_set_state @ Q @ B ) ) ) ) ).
% pairwise_mono
thf(fact_149_pairwise__mono,axiom,
! [P: state > state > $o,A: set_state,Q: state > state > $o,B: set_state] :
( ( pairwise_state @ P @ A )
=> ( ! [X: state,Y2: state] :
( ( P @ X @ Y2 )
=> ( Q @ X @ Y2 ) )
=> ( ( ord_le2494988322063910608_state @ B @ A )
=> ( pairwise_state @ Q @ B ) ) ) ) ).
% pairwise_mono
thf(fact_150_atMost__eq__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( ( set_or5536065684288934121_state @ X2 )
= ( set_or5536065684288934121_state @ Y ) )
= ( X2 = Y ) ) ).
% atMost_eq_iff
thf(fact_151_atLeast__eq__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( ( set_or6477372120337742821_state @ X2 )
= ( set_or6477372120337742821_state @ Y ) )
= ( X2 = Y ) ) ).
% atLeast_eq_iff
thf(fact_152_atMost__iff,axiom,
! [I: $o > set_state,K: $o > set_state] :
( ( member_o_set_state @ I @ ( set_or7255946770513471040_state @ K ) )
= ( ord_le9189382018855386905_state @ I @ K ) ) ).
% atMost_iff
thf(fact_153_atMost__iff,axiom,
! [I: set_set_state,K: set_set_state] :
( ( member_set_set_state @ I @ ( set_or8190520063335472031_state @ K ) )
= ( ord_le5175021213330142598_state @ I @ K ) ) ).
% atMost_iff
thf(fact_154_atMost__iff,axiom,
! [I: set_state,K: set_state] :
( ( member_set_state @ I @ ( set_or5536065684288934121_state @ K ) )
= ( ord_le2494988322063910608_state @ I @ K ) ) ).
% atMost_iff
thf(fact_155_atLeast__iff,axiom,
! [I: $o > set_state,K: $o > set_state] :
( ( member_o_set_state @ I @ ( set_or8064825548156300868_state @ K ) )
= ( ord_le9189382018855386905_state @ K @ I ) ) ).
% atLeast_iff
thf(fact_156_atLeast__iff,axiom,
! [I: set_set_state,K: set_set_state] :
( ( member_set_set_state @ I @ ( set_or922425460254742171_state @ K ) )
= ( ord_le5175021213330142598_state @ K @ I ) ) ).
% atLeast_iff
thf(fact_157_atLeast__iff,axiom,
! [I: set_state,K: set_state] :
( ( member_set_state @ I @ ( set_or6477372120337742821_state @ K ) )
= ( ord_le2494988322063910608_state @ K @ I ) ) ).
% atLeast_iff
thf(fact_158_Ioi__le__Ico,axiom,
! [A2: set_state] : ( ord_le5175021213330142598_state @ ( set_or7996350251103833098_state @ A2 ) @ ( set_or6477372120337742821_state @ A2 ) ) ).
% Ioi_le_Ico
thf(fact_159_pairwiseD,axiom,
! [R: set_state > set_state > $o,S: set_set_state,X2: set_state,Y: set_state] :
( ( pairwise_set_state @ R @ S )
=> ( ( member_set_state @ X2 @ S )
=> ( ( member_set_state @ Y @ S )
=> ( ( X2 != Y )
=> ( R @ X2 @ Y ) ) ) ) ) ).
% pairwiseD
thf(fact_160_pairwiseD,axiom,
! [R: set_set_state > set_set_state > $o,S: set_set_set_state,X2: set_set_state,Y: set_set_state] :
( ( pairwi6477347089298328827_state @ R @ S )
=> ( ( member_set_set_state @ X2 @ S )
=> ( ( member_set_set_state @ Y @ S )
=> ( ( X2 != Y )
=> ( R @ X2 @ Y ) ) ) ) ) ).
% pairwiseD
thf(fact_161_pairwiseD,axiom,
! [R: state > state > $o,S: set_state,X2: state,Y: state] :
( ( pairwise_state @ R @ S )
=> ( ( member_state @ X2 @ S )
=> ( ( member_state @ Y @ S )
=> ( ( X2 != Y )
=> ( R @ X2 @ Y ) ) ) ) ) ).
% pairwiseD
thf(fact_162_pairwiseI,axiom,
! [S: set_set_state,R: set_state > set_state > $o] :
( ! [X: set_state,Y2: set_state] :
( ( member_set_state @ X @ S )
=> ( ( member_set_state @ Y2 @ S )
=> ( ( X != Y2 )
=> ( R @ X @ Y2 ) ) ) )
=> ( pairwise_set_state @ R @ S ) ) ).
% pairwiseI
thf(fact_163_pairwiseI,axiom,
! [S: set_set_set_state,R: set_set_state > set_set_state > $o] :
( ! [X: set_set_state,Y2: set_set_state] :
( ( member_set_set_state @ X @ S )
=> ( ( member_set_set_state @ Y2 @ S )
=> ( ( X != Y2 )
=> ( R @ X @ Y2 ) ) ) )
=> ( pairwi6477347089298328827_state @ R @ S ) ) ).
% pairwiseI
thf(fact_164_pairwiseI,axiom,
! [S: set_state,R: state > state > $o] :
( ! [X: state,Y2: state] :
( ( member_state @ X @ S )
=> ( ( member_state @ Y2 @ S )
=> ( ( X != Y2 )
=> ( R @ X @ Y2 ) ) ) )
=> ( pairwise_state @ R @ S ) ) ).
% pairwiseI
thf(fact_165_pairwise__def,axiom,
( pairwise_state
= ( ^ [R2: state > state > $o,S2: set_state] :
! [X3: state] :
( ( member_state @ X3 @ S2 )
=> ! [Y4: state] :
( ( member_state @ Y4 @ S2 )
=> ( ( X3 != Y4 )
=> ( R2 @ X3 @ Y4 ) ) ) ) ) ) ).
% pairwise_def
thf(fact_166_partial__preordering__def,axiom,
( partia7871104319988624314_state
= ( ^ [Less_eq: set_state > set_state > $o] :
( ! [A4: set_state] : ( Less_eq @ A4 @ A4 )
& ! [A4: set_state,B4: set_state,C3: set_state] :
( ( Less_eq @ A4 @ B4 )
=> ( ( Less_eq @ B4 @ C3 )
=> ( Less_eq @ A4 @ C3 ) ) ) ) ) ) ).
% partial_preordering_def
thf(fact_167_partial__preordering_Otrans,axiom,
! [Less_eq2: set_state > set_state > $o,A2: set_state,B3: set_state,C: set_state] :
( ( partia7871104319988624314_state @ Less_eq2 )
=> ( ( Less_eq2 @ A2 @ B3 )
=> ( ( Less_eq2 @ B3 @ C )
=> ( Less_eq2 @ A2 @ C ) ) ) ) ).
% partial_preordering.trans
thf(fact_168_partial__preordering_Ointro,axiom,
! [Less_eq2: set_state > set_state > $o] :
( ! [A5: set_state] : ( Less_eq2 @ A5 @ A5 )
=> ( ! [A5: set_state,B5: set_state,C4: set_state] :
( ( Less_eq2 @ A5 @ B5 )
=> ( ( Less_eq2 @ B5 @ C4 )
=> ( Less_eq2 @ A5 @ C4 ) ) )
=> ( partia7871104319988624314_state @ Less_eq2 ) ) ) ).
% partial_preordering.intro
thf(fact_169_partial__preordering_Orefl,axiom,
! [Less_eq2: set_state > set_state > $o,A2: set_state] :
( ( partia7871104319988624314_state @ Less_eq2 )
=> ( Less_eq2 @ A2 @ A2 ) ) ).
% partial_preordering.refl
thf(fact_170_Icc__subset__Ici__iff,axiom,
! [L: $o > set_state,H: $o > set_state,L2: $o > set_state] :
( ( ord_le4652835513209282297_state @ ( set_or7399831441507084590_state @ L @ H ) @ ( set_or8064825548156300868_state @ L2 ) )
= ( ~ ( ord_le9189382018855386905_state @ L @ H )
| ( ord_le9189382018855386905_state @ L2 @ L ) ) ) ).
% Icc_subset_Ici_iff
thf(fact_171_Icc__subset__Ici__iff,axiom,
! [L: set_set_state,H: set_set_state,L2: set_set_state] :
( ( ord_le3154822624800881980_state @ ( set_or7796883608616495921_state @ L @ H ) @ ( set_or922425460254742171_state @ L2 ) )
= ( ~ ( ord_le5175021213330142598_state @ L @ H )
| ( ord_le5175021213330142598_state @ L2 @ L ) ) ) ).
% Icc_subset_Ici_iff
thf(fact_172_Icc__subset__Ici__iff,axiom,
! [L: set_state,H: set_state,L2: set_state] :
( ( ord_le5175021213330142598_state @ ( set_or701696889746204795_state @ L @ H ) @ ( set_or6477372120337742821_state @ L2 ) )
= ( ~ ( ord_le2494988322063910608_state @ L @ H )
| ( ord_le2494988322063910608_state @ L2 @ L ) ) ) ).
% Icc_subset_Ici_iff
thf(fact_173_Icc__subset__Iic__iff,axiom,
! [L: $o > set_state,H: $o > set_state,H2: $o > set_state] :
( ( ord_le4652835513209282297_state @ ( set_or7399831441507084590_state @ L @ H ) @ ( set_or7255946770513471040_state @ H2 ) )
= ( ~ ( ord_le9189382018855386905_state @ L @ H )
| ( ord_le9189382018855386905_state @ H @ H2 ) ) ) ).
% Icc_subset_Iic_iff
thf(fact_174_Icc__subset__Iic__iff,axiom,
! [L: set_set_state,H: set_set_state,H2: set_set_state] :
( ( ord_le3154822624800881980_state @ ( set_or7796883608616495921_state @ L @ H ) @ ( set_or8190520063335472031_state @ H2 ) )
= ( ~ ( ord_le5175021213330142598_state @ L @ H )
| ( ord_le5175021213330142598_state @ H @ H2 ) ) ) ).
% Icc_subset_Iic_iff
thf(fact_175_Icc__subset__Iic__iff,axiom,
! [L: set_state,H: set_state,H2: set_state] :
( ( ord_le5175021213330142598_state @ ( set_or701696889746204795_state @ L @ H ) @ ( set_or5536065684288934121_state @ H2 ) )
= ( ~ ( ord_le2494988322063910608_state @ L @ H )
| ( ord_le2494988322063910608_state @ H @ H2 ) ) ) ).
% Icc_subset_Iic_iff
thf(fact_176_top__apply,axiom,
( top_top_state_o
= ( ^ [X3: state] : top_top_o ) ) ).
% top_apply
thf(fact_177_atMost__UNIV__triv,axiom,
( ( set_or8190520063335472031_state @ top_to5262587396890829782_state )
= top_to3598970937283095436_state ) ).
% atMost_UNIV_triv
thf(fact_178_atMost__UNIV__triv,axiom,
( ( set_or5536065684288934121_state @ top_top_set_state )
= top_to5262587396890829782_state ) ).
% atMost_UNIV_triv
thf(fact_179_UNIV__I,axiom,
! [X2: set_set_state] : ( member_set_set_state @ X2 @ top_to3598970937283095436_state ) ).
% UNIV_I
thf(fact_180_UNIV__I,axiom,
! [X2: set_state] : ( member_set_state @ X2 @ top_to5262587396890829782_state ) ).
% UNIV_I
thf(fact_181_UNIV__I,axiom,
! [X2: state] : ( member_state @ X2 @ top_top_set_state ) ).
% UNIV_I
thf(fact_182_psubsetI,axiom,
! [A: set_set_state,B: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ B )
=> ( ( A != B )
=> ( ord_le8280034978549525370_state @ A @ B ) ) ) ).
% psubsetI
thf(fact_183_psubsetI,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_state @ A @ B ) ) ) ).
% psubsetI
thf(fact_184_Compl__eq__Compl__iff,axiom,
! [A: set_state,B: set_state] :
( ( ( uminus472742206872269241_state @ A )
= ( uminus472742206872269241_state @ B ) )
= ( A = B ) ) ).
% Compl_eq_Compl_iff
thf(fact_185_Compl__iff,axiom,
! [C: set_state,A: set_set_state] :
( ( member_set_state @ C @ ( uminus4035512285888117871_state @ A ) )
= ( ~ ( member_set_state @ C @ A ) ) ) ).
% Compl_iff
thf(fact_186_Compl__iff,axiom,
! [C: set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ C @ ( uminus2384571021370171429_state @ A ) )
= ( ~ ( member_set_set_state @ C @ A ) ) ) ).
% Compl_iff
thf(fact_187_Compl__iff,axiom,
! [C: state,A: set_state] :
( ( member_state @ C @ ( uminus472742206872269241_state @ A ) )
= ( ~ ( member_state @ C @ A ) ) ) ).
% Compl_iff
thf(fact_188_ComplI,axiom,
! [C: set_state,A: set_set_state] :
( ~ ( member_set_state @ C @ A )
=> ( member_set_state @ C @ ( uminus4035512285888117871_state @ A ) ) ) ).
% ComplI
thf(fact_189_ComplI,axiom,
! [C: set_set_state,A: set_set_set_state] :
( ~ ( member_set_set_state @ C @ A )
=> ( member_set_set_state @ C @ ( uminus2384571021370171429_state @ A ) ) ) ).
% ComplI
thf(fact_190_ComplI,axiom,
! [C: state,A: set_state] :
( ~ ( member_state @ C @ A )
=> ( member_state @ C @ ( uminus472742206872269241_state @ A ) ) ) ).
% ComplI
thf(fact_191_atLeastAtMost__iff,axiom,
! [I: $o > set_state,L: $o > set_state,U: $o > set_state] :
( ( member_o_set_state @ I @ ( set_or7399831441507084590_state @ L @ U ) )
= ( ( ord_le9189382018855386905_state @ L @ I )
& ( ord_le9189382018855386905_state @ I @ U ) ) ) ).
% atLeastAtMost_iff
thf(fact_192_atLeastAtMost__iff,axiom,
! [I: set_set_state,L: set_set_state,U: set_set_state] :
( ( member_set_set_state @ I @ ( set_or7796883608616495921_state @ L @ U ) )
= ( ( ord_le5175021213330142598_state @ L @ I )
& ( ord_le5175021213330142598_state @ I @ U ) ) ) ).
% atLeastAtMost_iff
thf(fact_193_atLeastAtMost__iff,axiom,
! [I: set_state,L: set_state,U: set_state] :
( ( member_set_state @ I @ ( set_or701696889746204795_state @ L @ U ) )
= ( ( ord_le2494988322063910608_state @ L @ I )
& ( ord_le2494988322063910608_state @ I @ U ) ) ) ).
% atLeastAtMost_iff
thf(fact_194_Icc__eq__Icc,axiom,
! [L: $o > set_state,H: $o > set_state,L2: $o > set_state,H2: $o > set_state] :
( ( ( set_or7399831441507084590_state @ L @ H )
= ( set_or7399831441507084590_state @ L2 @ H2 ) )
= ( ( ( L = L2 )
& ( H = H2 ) )
| ( ~ ( ord_le9189382018855386905_state @ L @ H )
& ~ ( ord_le9189382018855386905_state @ L2 @ H2 ) ) ) ) ).
% Icc_eq_Icc
thf(fact_195_Icc__eq__Icc,axiom,
! [L: set_set_state,H: set_set_state,L2: set_set_state,H2: set_set_state] :
( ( ( set_or7796883608616495921_state @ L @ H )
= ( set_or7796883608616495921_state @ L2 @ H2 ) )
= ( ( ( L = L2 )
& ( H = H2 ) )
| ( ~ ( ord_le5175021213330142598_state @ L @ H )
& ~ ( ord_le5175021213330142598_state @ L2 @ H2 ) ) ) ) ).
% Icc_eq_Icc
thf(fact_196_Icc__eq__Icc,axiom,
! [L: set_state,H: set_state,L2: set_state,H2: set_state] :
( ( ( set_or701696889746204795_state @ L @ H )
= ( set_or701696889746204795_state @ L2 @ H2 ) )
= ( ( ( L = L2 )
& ( H = H2 ) )
| ( ~ ( ord_le2494988322063910608_state @ L @ H )
& ~ ( ord_le2494988322063910608_state @ L2 @ H2 ) ) ) ) ).
% Icc_eq_Icc
thf(fact_197_lessThan__iff,axiom,
! [I: set_state,K: set_state] :
( ( member_set_state @ I @ ( set_or1034127368735114509_state @ K ) )
= ( ord_less_set_state @ I @ K ) ) ).
% lessThan_iff
thf(fact_198_lessThan__iff,axiom,
! [I: set_set_state,K: set_set_state] :
( ( member_set_set_state @ I @ ( set_or5856722414167211971_state @ K ) )
= ( ord_le8280034978549525370_state @ I @ K ) ) ).
% lessThan_iff
thf(fact_199_Compl__subset__Compl__iff,axiom,
! [A: set_set_state,B: set_set_state] :
( ( ord_le5175021213330142598_state @ ( uminus4035512285888117871_state @ A ) @ ( uminus4035512285888117871_state @ B ) )
= ( ord_le5175021213330142598_state @ B @ A ) ) ).
% Compl_subset_Compl_iff
thf(fact_200_Compl__subset__Compl__iff,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ A ) @ ( uminus472742206872269241_state @ B ) )
= ( ord_le2494988322063910608_state @ B @ A ) ) ).
% Compl_subset_Compl_iff
thf(fact_201_Compl__anti__mono,axiom,
! [A: set_set_state,B: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ B )
=> ( ord_le5175021213330142598_state @ ( uminus4035512285888117871_state @ B ) @ ( uminus4035512285888117871_state @ A ) ) ) ).
% Compl_anti_mono
thf(fact_202_Compl__anti__mono,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ B ) @ ( uminus472742206872269241_state @ A ) ) ) ).
% Compl_anti_mono
thf(fact_203_greaterThan__iff,axiom,
! [I: set_state,K: set_state] :
( ( member_set_state @ I @ ( set_or7996350251103833098_state @ K ) )
= ( ord_less_set_state @ K @ I ) ) ).
% greaterThan_iff
thf(fact_204_greaterThan__iff,axiom,
! [I: set_set_state,K: set_set_state] :
( ( member_set_set_state @ I @ ( set_or8484835426764182208_state @ K ) )
= ( ord_le8280034978549525370_state @ K @ I ) ) ).
% greaterThan_iff
thf(fact_205_atLeastLessThan__iff,axiom,
! [I: $o > set_state,L: $o > set_state,U: $o > set_state] :
( ( member_o_set_state @ I @ ( set_or8134177505681183498_state @ L @ U ) )
= ( ( ord_le9189382018855386905_state @ L @ I )
& ( ord_less_o_set_state @ I @ U ) ) ) ).
% atLeastLessThan_iff
thf(fact_206_atLeastLessThan__iff,axiom,
! [I: set_set_state,L: set_set_state,U: set_set_state] :
( ( member_set_set_state @ I @ ( set_or5996981303281673813_state @ L @ U ) )
= ( ( ord_le5175021213330142598_state @ L @ I )
& ( ord_le8280034978549525370_state @ I @ U ) ) ) ).
% atLeastLessThan_iff
thf(fact_207_atLeastLessThan__iff,axiom,
! [I: set_state,L: set_state,U: set_state] :
( ( member_set_state @ I @ ( set_or2838015025653527455_state @ L @ U ) )
= ( ( ord_le2494988322063910608_state @ L @ I )
& ( ord_less_set_state @ I @ U ) ) ) ).
% atLeastLessThan_iff
thf(fact_208_atLeastatMost__subset__iff,axiom,
! [A2: $o > set_state,B3: $o > set_state,C: $o > set_state,D: $o > set_state] :
( ( ord_le4652835513209282297_state @ ( set_or7399831441507084590_state @ A2 @ B3 ) @ ( set_or7399831441507084590_state @ C @ D ) )
= ( ~ ( ord_le9189382018855386905_state @ A2 @ B3 )
| ( ( ord_le9189382018855386905_state @ C @ A2 )
& ( ord_le9189382018855386905_state @ B3 @ D ) ) ) ) ).
% atLeastatMost_subset_iff
thf(fact_209_atLeastatMost__subset__iff,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state,D: set_set_state] :
( ( ord_le3154822624800881980_state @ ( set_or7796883608616495921_state @ A2 @ B3 ) @ ( set_or7796883608616495921_state @ C @ D ) )
= ( ~ ( ord_le5175021213330142598_state @ A2 @ B3 )
| ( ( ord_le5175021213330142598_state @ C @ A2 )
& ( ord_le5175021213330142598_state @ B3 @ D ) ) ) ) ).
% atLeastatMost_subset_iff
thf(fact_210_atLeastatMost__subset__iff,axiom,
! [A2: set_state,B3: set_state,C: set_state,D: set_state] :
( ( ord_le5175021213330142598_state @ ( set_or701696889746204795_state @ A2 @ B3 ) @ ( set_or701696889746204795_state @ C @ D ) )
= ( ~ ( ord_le2494988322063910608_state @ A2 @ B3 )
| ( ( ord_le2494988322063910608_state @ C @ A2 )
& ( ord_le2494988322063910608_state @ B3 @ D ) ) ) ) ).
% atLeastatMost_subset_iff
thf(fact_211_atLeastatMost__psubset__iff,axiom,
! [A2: $o > set_state,B3: $o > set_state,C: $o > set_state,D: $o > set_state] :
( ( ord_le3245661169210212869_state @ ( set_or7399831441507084590_state @ A2 @ B3 ) @ ( set_or7399831441507084590_state @ C @ D ) )
= ( ( ~ ( ord_le9189382018855386905_state @ A2 @ B3 )
| ( ( ord_le9189382018855386905_state @ C @ A2 )
& ( ord_le9189382018855386905_state @ B3 @ D )
& ( ( ord_less_o_set_state @ C @ A2 )
| ( ord_less_o_set_state @ B3 @ D ) ) ) )
& ( ord_le9189382018855386905_state @ C @ D ) ) ) ).
% atLeastatMost_psubset_iff
thf(fact_212_atLeastatMost__psubset__iff,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state,D: set_set_state] :
( ( ord_le6814633228373517104_state @ ( set_or7796883608616495921_state @ A2 @ B3 ) @ ( set_or7796883608616495921_state @ C @ D ) )
= ( ( ~ ( ord_le5175021213330142598_state @ A2 @ B3 )
| ( ( ord_le5175021213330142598_state @ C @ A2 )
& ( ord_le5175021213330142598_state @ B3 @ D )
& ( ( ord_le8280034978549525370_state @ C @ A2 )
| ( ord_le8280034978549525370_state @ B3 @ D ) ) ) )
& ( ord_le5175021213330142598_state @ C @ D ) ) ) ).
% atLeastatMost_psubset_iff
thf(fact_213_atLeastatMost__psubset__iff,axiom,
! [A2: set_state,B3: set_state,C: set_state,D: set_state] :
( ( ord_le8280034978549525370_state @ ( set_or701696889746204795_state @ A2 @ B3 ) @ ( set_or701696889746204795_state @ C @ D ) )
= ( ( ~ ( ord_le2494988322063910608_state @ A2 @ B3 )
| ( ( ord_le2494988322063910608_state @ C @ A2 )
& ( ord_le2494988322063910608_state @ B3 @ D )
& ( ( ord_less_set_state @ C @ A2 )
| ( ord_less_set_state @ B3 @ D ) ) ) )
& ( ord_le2494988322063910608_state @ C @ D ) ) ) ).
% atLeastatMost_psubset_iff
thf(fact_214_verit__comp__simplify1_I1_J,axiom,
! [A2: set_state] :
~ ( ord_less_set_state @ A2 @ A2 ) ).
% verit_comp_simplify1(1)
thf(fact_215_verit__comp__simplify1_I1_J,axiom,
! [A2: set_set_state] :
~ ( ord_le8280034978549525370_state @ A2 @ A2 ) ).
% verit_comp_simplify1(1)
thf(fact_216_order__less__imp__not__less,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ~ ( ord_less_set_state @ Y @ X2 ) ) ).
% order_less_imp_not_less
thf(fact_217_order__less__imp__not__less,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ~ ( ord_le8280034978549525370_state @ Y @ X2 ) ) ).
% order_less_imp_not_less
thf(fact_218_order__less__imp__not__eq2,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ( Y != X2 ) ) ).
% order_less_imp_not_eq2
thf(fact_219_order__less__imp__not__eq2,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ( Y != X2 ) ) ).
% order_less_imp_not_eq2
thf(fact_220_order__less__imp__not__eq,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ( X2 != Y ) ) ).
% order_less_imp_not_eq
thf(fact_221_order__less__imp__not__eq,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ( X2 != Y ) ) ).
% order_less_imp_not_eq
thf(fact_222_order__less__imp__triv,axiom,
! [X2: set_state,Y: set_state,P: $o] :
( ( ord_less_set_state @ X2 @ Y )
=> ( ( ord_less_set_state @ Y @ X2 )
=> P ) ) ).
% order_less_imp_triv
thf(fact_223_order__less__imp__triv,axiom,
! [X2: set_set_state,Y: set_set_state,P: $o] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ( ( ord_le8280034978549525370_state @ Y @ X2 )
=> P ) ) ).
% order_less_imp_triv
thf(fact_224_order__less__not__sym,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ~ ( ord_less_set_state @ Y @ X2 ) ) ).
% order_less_not_sym
thf(fact_225_order__less__not__sym,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ~ ( ord_le8280034978549525370_state @ Y @ X2 ) ) ).
% order_less_not_sym
thf(fact_226_order__less__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_state,C: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( ord_less_set_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_subst2
thf(fact_227_order__less__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_set_state,C: set_set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( ord_le8280034978549525370_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_subst2
thf(fact_228_order__less__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_state,C: set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( ord_less_set_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_subst2
thf(fact_229_order__less__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( ord_le8280034978549525370_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_subst2
thf(fact_230_order__less__subst1,axiom,
! [A2: set_state,F: set_state > set_state,B3: set_state,C: set_state] :
( ( ord_less_set_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_subst1
thf(fact_231_order__less__subst1,axiom,
! [A2: set_state,F: set_set_state > set_state,B3: set_set_state,C: set_set_state] :
( ( ord_less_set_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_subst1
thf(fact_232_order__less__subst1,axiom,
! [A2: set_set_state,F: set_state > set_set_state,B3: set_state,C: set_state] :
( ( ord_le8280034978549525370_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_subst1
thf(fact_233_order__less__subst1,axiom,
! [A2: set_set_state,F: set_set_state > set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_subst1
thf(fact_234_order__less__irrefl,axiom,
! [X2: set_state] :
~ ( ord_less_set_state @ X2 @ X2 ) ).
% order_less_irrefl
thf(fact_235_order__less__irrefl,axiom,
! [X2: set_set_state] :
~ ( ord_le8280034978549525370_state @ X2 @ X2 ) ).
% order_less_irrefl
thf(fact_236_ord__less__eq__subst,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_state,C: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_less_eq_subst
thf(fact_237_ord__less__eq__subst,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_set_state,C: set_set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_less_eq_subst
thf(fact_238_ord__less__eq__subst,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_state,C: set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_less_eq_subst
thf(fact_239_ord__less__eq__subst,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( ( F @ B3 )
= C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_less_eq_subst
thf(fact_240_ord__eq__less__subst,axiom,
! [A2: set_state,F: set_state > set_state,B3: set_state,C: set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_less_subst
thf(fact_241_ord__eq__less__subst,axiom,
! [A2: set_set_state,F: set_state > set_set_state,B3: set_state,C: set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_less_subst
thf(fact_242_ord__eq__less__subst,axiom,
! [A2: set_state,F: set_set_state > set_state,B3: set_set_state,C: set_set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_less_subst
thf(fact_243_ord__eq__less__subst,axiom,
! [A2: set_set_state,F: set_set_state > set_set_state,B3: set_set_state,C: set_set_state] :
( ( A2
= ( F @ B3 ) )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_less_subst
thf(fact_244_order__less__trans,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ( ( ord_less_set_state @ Y @ Z2 )
=> ( ord_less_set_state @ X2 @ Z2 ) ) ) ).
% order_less_trans
thf(fact_245_order__less__trans,axiom,
! [X2: set_set_state,Y: set_set_state,Z2: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ( ( ord_le8280034978549525370_state @ Y @ Z2 )
=> ( ord_le8280034978549525370_state @ X2 @ Z2 ) ) ) ).
% order_less_trans
thf(fact_246_order__less__asym_H,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ~ ( ord_less_set_state @ B3 @ A2 ) ) ).
% order_less_asym'
thf(fact_247_order__less__asym_H,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ~ ( ord_le8280034978549525370_state @ B3 @ A2 ) ) ).
% order_less_asym'
thf(fact_248_order__less__asym,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ~ ( ord_less_set_state @ Y @ X2 ) ) ).
% order_less_asym
thf(fact_249_order__less__asym,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ~ ( ord_le8280034978549525370_state @ Y @ X2 ) ) ).
% order_less_asym
thf(fact_250_double__complement,axiom,
! [A: set_state] :
( ( uminus472742206872269241_state @ ( uminus472742206872269241_state @ A ) )
= A ) ).
% double_complement
thf(fact_251_UNIV__witness,axiom,
? [X: set_set_state] : ( member_set_set_state @ X @ top_to3598970937283095436_state ) ).
% UNIV_witness
thf(fact_252_UNIV__witness,axiom,
? [X: set_state] : ( member_set_state @ X @ top_to5262587396890829782_state ) ).
% UNIV_witness
thf(fact_253_UNIV__witness,axiom,
? [X: state] : ( member_state @ X @ top_top_set_state ) ).
% UNIV_witness
thf(fact_254_UNIV__eq__I,axiom,
! [A: set_set_set_state] :
( ! [X: set_set_state] : ( member_set_set_state @ X @ A )
=> ( top_to3598970937283095436_state = A ) ) ).
% UNIV_eq_I
thf(fact_255_UNIV__eq__I,axiom,
! [A: set_set_state] :
( ! [X: set_state] : ( member_set_state @ X @ A )
=> ( top_to5262587396890829782_state = A ) ) ).
% UNIV_eq_I
thf(fact_256_UNIV__eq__I,axiom,
! [A: set_state] :
( ! [X: state] : ( member_state @ X @ A )
=> ( top_top_set_state = A ) ) ).
% UNIV_eq_I
thf(fact_257_ComplD,axiom,
! [C: set_state,A: set_set_state] :
( ( member_set_state @ C @ ( uminus4035512285888117871_state @ A ) )
=> ~ ( member_set_state @ C @ A ) ) ).
% ComplD
thf(fact_258_ComplD,axiom,
! [C: set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ C @ ( uminus2384571021370171429_state @ A ) )
=> ~ ( member_set_set_state @ C @ A ) ) ).
% ComplD
thf(fact_259_ComplD,axiom,
! [C: state,A: set_state] :
( ( member_state @ C @ ( uminus472742206872269241_state @ A ) )
=> ~ ( member_state @ C @ A ) ) ).
% ComplD
thf(fact_260_dual__order_Ostrict__implies__not__eq,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_less_set_state @ B3 @ A2 )
=> ( A2 != B3 ) ) ).
% dual_order.strict_implies_not_eq
thf(fact_261_dual__order_Ostrict__implies__not__eq,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( ord_le8280034978549525370_state @ B3 @ A2 )
=> ( A2 != B3 ) ) ).
% dual_order.strict_implies_not_eq
thf(fact_262_order_Ostrict__implies__not__eq,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( A2 != B3 ) ) ).
% order.strict_implies_not_eq
thf(fact_263_order_Ostrict__implies__not__eq,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( A2 != B3 ) ) ).
% order.strict_implies_not_eq
thf(fact_264_dual__order_Ostrict__trans,axiom,
! [B3: set_state,A2: set_state,C: set_state] :
( ( ord_less_set_state @ B3 @ A2 )
=> ( ( ord_less_set_state @ C @ B3 )
=> ( ord_less_set_state @ C @ A2 ) ) ) ).
% dual_order.strict_trans
thf(fact_265_dual__order_Ostrict__trans,axiom,
! [B3: set_set_state,A2: set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ B3 @ A2 )
=> ( ( ord_le8280034978549525370_state @ C @ B3 )
=> ( ord_le8280034978549525370_state @ C @ A2 ) ) ) ).
% dual_order.strict_trans
thf(fact_266_top_Onot__eq__extremum,axiom,
! [A2: state > $o] :
( ( A2 != top_top_state_o )
= ( ord_less_state_o @ A2 @ top_top_state_o ) ) ).
% top.not_eq_extremum
thf(fact_267_top_Onot__eq__extremum,axiom,
! [A2: set_state] :
( ( A2 != top_top_set_state )
= ( ord_less_set_state @ A2 @ top_top_set_state ) ) ).
% top.not_eq_extremum
thf(fact_268_top_Onot__eq__extremum,axiom,
! [A2: set_set_state] :
( ( A2 != top_to5262587396890829782_state )
= ( ord_le8280034978549525370_state @ A2 @ top_to5262587396890829782_state ) ) ).
% top.not_eq_extremum
thf(fact_269_top_Oextremum__strict,axiom,
! [A2: state > $o] :
~ ( ord_less_state_o @ top_top_state_o @ A2 ) ).
% top.extremum_strict
thf(fact_270_top_Oextremum__strict,axiom,
! [A2: set_state] :
~ ( ord_less_set_state @ top_top_set_state @ A2 ) ).
% top.extremum_strict
thf(fact_271_top_Oextremum__strict,axiom,
! [A2: set_set_state] :
~ ( ord_le8280034978549525370_state @ top_to5262587396890829782_state @ A2 ) ).
% top.extremum_strict
thf(fact_272_order_Ostrict__trans,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ord_less_set_state @ A2 @ C ) ) ) ).
% order.strict_trans
thf(fact_273_order_Ostrict__trans,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ord_le8280034978549525370_state @ A2 @ C ) ) ) ).
% order.strict_trans
thf(fact_274_dual__order_Oirrefl,axiom,
! [A2: set_state] :
~ ( ord_less_set_state @ A2 @ A2 ) ).
% dual_order.irrefl
thf(fact_275_dual__order_Oirrefl,axiom,
! [A2: set_set_state] :
~ ( ord_le8280034978549525370_state @ A2 @ A2 ) ).
% dual_order.irrefl
thf(fact_276_dual__order_Oasym,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_less_set_state @ B3 @ A2 )
=> ~ ( ord_less_set_state @ A2 @ B3 ) ) ).
% dual_order.asym
thf(fact_277_dual__order_Oasym,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( ord_le8280034978549525370_state @ B3 @ A2 )
=> ~ ( ord_le8280034978549525370_state @ A2 @ B3 ) ) ).
% dual_order.asym
thf(fact_278_ord__less__eq__trans,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( B3 = C )
=> ( ord_less_set_state @ A2 @ C ) ) ) ).
% ord_less_eq_trans
thf(fact_279_ord__less__eq__trans,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( B3 = C )
=> ( ord_le8280034978549525370_state @ A2 @ C ) ) ) ).
% ord_less_eq_trans
thf(fact_280_ord__eq__less__trans,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( A2 = B3 )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ord_less_set_state @ A2 @ C ) ) ) ).
% ord_eq_less_trans
thf(fact_281_ord__eq__less__trans,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state] :
( ( A2 = B3 )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ord_le8280034978549525370_state @ A2 @ C ) ) ) ).
% ord_eq_less_trans
thf(fact_282_order_Oasym,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ~ ( ord_less_set_state @ B3 @ A2 ) ) ).
% order.asym
thf(fact_283_order_Oasym,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ~ ( ord_le8280034978549525370_state @ B3 @ A2 ) ) ).
% order.asym
thf(fact_284_less__imp__neq,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ( X2 != Y ) ) ).
% less_imp_neq
thf(fact_285_less__imp__neq,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ( X2 != Y ) ) ).
% less_imp_neq
thf(fact_286_atMost__eq__UNIV__iff,axiom,
! [X2: state > $o] :
( ( ( set_or1722117244622138588tate_o @ X2 )
= top_top_set_state_o2 )
= ( X2 = top_top_state_o ) ) ).
% atMost_eq_UNIV_iff
thf(fact_287_atMost__eq__UNIV__iff,axiom,
! [X2: set_set_state] :
( ( ( set_or8190520063335472031_state @ X2 )
= top_to3598970937283095436_state )
= ( X2 = top_to5262587396890829782_state ) ) ).
% atMost_eq_UNIV_iff
thf(fact_288_atMost__eq__UNIV__iff,axiom,
! [X2: set_state] :
( ( ( set_or5536065684288934121_state @ X2 )
= top_to5262587396890829782_state )
= ( X2 = top_top_set_state ) ) ).
% atMost_eq_UNIV_iff
thf(fact_289_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
! [A2: $o > set_state,B3: $o > set_state,C: $o > set_state,D: $o > set_state] :
( ( ord_le4652835513209282297_state @ ( set_or7399831441507084590_state @ A2 @ B3 ) @ ( set_or8134177505681183498_state @ C @ D ) )
= ( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_le9189382018855386905_state @ C @ A2 )
& ( ord_less_o_set_state @ B3 @ D ) ) ) ) ).
% atLeastAtMost_subseteq_atLeastLessThan_iff
thf(fact_290_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state,D: set_set_state] :
( ( ord_le3154822624800881980_state @ ( set_or7796883608616495921_state @ A2 @ B3 ) @ ( set_or5996981303281673813_state @ C @ D ) )
= ( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_le5175021213330142598_state @ C @ A2 )
& ( ord_le8280034978549525370_state @ B3 @ D ) ) ) ) ).
% atLeastAtMost_subseteq_atLeastLessThan_iff
thf(fact_291_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
! [A2: set_state,B3: set_state,C: set_state,D: set_state] :
( ( ord_le5175021213330142598_state @ ( set_or701696889746204795_state @ A2 @ B3 ) @ ( set_or2838015025653527455_state @ C @ D ) )
= ( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ C @ A2 )
& ( ord_less_set_state @ B3 @ D ) ) ) ) ).
% atLeastAtMost_subseteq_atLeastLessThan_iff
thf(fact_292_top_Oextremum__uniqueI,axiom,
! [A2: state > $o] :
( ( ord_less_eq_state_o @ top_top_state_o @ A2 )
=> ( A2 = top_top_state_o ) ) ).
% top.extremum_uniqueI
thf(fact_293_top_Oextremum__uniqueI,axiom,
! [A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ top_top_o_set_state @ A2 )
=> ( A2 = top_top_o_set_state ) ) ).
% top.extremum_uniqueI
thf(fact_294_top_Oextremum__uniqueI,axiom,
! [A2: set_set_state] :
( ( ord_le5175021213330142598_state @ top_to5262587396890829782_state @ A2 )
=> ( A2 = top_to5262587396890829782_state ) ) ).
% top.extremum_uniqueI
thf(fact_295_top_Oextremum__uniqueI,axiom,
! [A2: set_state] :
( ( ord_le2494988322063910608_state @ top_top_set_state @ A2 )
=> ( A2 = top_top_set_state ) ) ).
% top.extremum_uniqueI
thf(fact_296_top_Oextremum__unique,axiom,
! [A2: state > $o] :
( ( ord_less_eq_state_o @ top_top_state_o @ A2 )
= ( A2 = top_top_state_o ) ) ).
% top.extremum_unique
thf(fact_297_top_Oextremum__unique,axiom,
! [A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ top_top_o_set_state @ A2 )
= ( A2 = top_top_o_set_state ) ) ).
% top.extremum_unique
thf(fact_298_top_Oextremum__unique,axiom,
! [A2: set_set_state] :
( ( ord_le5175021213330142598_state @ top_to5262587396890829782_state @ A2 )
= ( A2 = top_to5262587396890829782_state ) ) ).
% top.extremum_unique
thf(fact_299_top_Oextremum__unique,axiom,
! [A2: set_state] :
( ( ord_le2494988322063910608_state @ top_top_set_state @ A2 )
= ( A2 = top_top_set_state ) ) ).
% top.extremum_unique
thf(fact_300_top__greatest,axiom,
! [A2: state > $o] : ( ord_less_eq_state_o @ A2 @ top_top_state_o ) ).
% top_greatest
thf(fact_301_top__greatest,axiom,
! [A2: $o > set_state] : ( ord_le9189382018855386905_state @ A2 @ top_top_o_set_state ) ).
% top_greatest
thf(fact_302_top__greatest,axiom,
! [A2: set_set_state] : ( ord_le5175021213330142598_state @ A2 @ top_to5262587396890829782_state ) ).
% top_greatest
thf(fact_303_top__greatest,axiom,
! [A2: set_state] : ( ord_le2494988322063910608_state @ A2 @ top_top_set_state ) ).
% top_greatest
thf(fact_304_order__le__imp__less__or__eq,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ Y )
=> ( ( ord_less_o_set_state @ X2 @ Y )
| ( X2 = Y ) ) ) ).
% order_le_imp_less_or_eq
thf(fact_305_order__le__imp__less__or__eq,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ Y )
=> ( ( ord_le8280034978549525370_state @ X2 @ Y )
| ( X2 = Y ) ) ) ).
% order_le_imp_less_or_eq
thf(fact_306_order__le__imp__less__or__eq,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( ord_less_set_state @ X2 @ Y )
| ( X2 = Y ) ) ) ).
% order_le_imp_less_or_eq
thf(fact_307_order__less__le__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_state,C: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_le_subst2
thf(fact_308_order__less__le__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_state,C: set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_le_subst2
thf(fact_309_order__less__le__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > $o > set_state,C: $o > set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( ord_le9189382018855386905_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_less_o_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_le_subst2
thf(fact_310_order__less__le__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > $o > set_state,C: $o > set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( ord_le9189382018855386905_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_less_o_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_le_subst2
thf(fact_311_order__less__le__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_set_state,C: set_set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( ord_le5175021213330142598_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_le_subst2
thf(fact_312_order__less__le__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( ord_le5175021213330142598_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_less_le_subst2
thf(fact_313_order__less__le__subst1,axiom,
! [A2: $o > set_state,F: set_state > $o > set_state,B3: set_state,C: set_state] :
( ( ord_less_o_set_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_314_order__less__le__subst1,axiom,
! [A2: set_set_state,F: set_state > set_set_state,B3: set_state,C: set_state] :
( ( ord_le8280034978549525370_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_315_order__less__le__subst1,axiom,
! [A2: set_state,F: ( $o > set_state ) > set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_less_set_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_316_order__less__le__subst1,axiom,
! [A2: $o > set_state,F: ( $o > set_state ) > $o > set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_less_o_set_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_317_order__less__le__subst1,axiom,
! [A2: set_set_state,F: ( $o > set_state ) > set_set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_le8280034978549525370_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_318_order__less__le__subst1,axiom,
! [A2: set_state,F: set_set_state > set_state,B3: set_set_state,C: set_set_state] :
( ( ord_less_set_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_319_order__less__le__subst1,axiom,
! [A2: $o > set_state,F: set_set_state > $o > set_state,B3: set_set_state,C: set_set_state] :
( ( ord_less_o_set_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_320_order__less__le__subst1,axiom,
! [A2: set_set_state,F: set_set_state > set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_321_order__less__le__subst1,axiom,
! [A2: set_state,F: set_state > set_state,B3: set_state,C: set_state] :
( ( ord_less_set_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_322_order__le__less__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > $o > set_state,C: $o > set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_less_o_set_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_323_order__le__less__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_set_state,C: set_set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_le8280034978549525370_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_324_order__le__less__subst2,axiom,
! [A2: $o > set_state,B3: $o > set_state,F: ( $o > set_state ) > set_state,C: set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_less_set_state @ ( F @ B3 ) @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_325_order__le__less__subst2,axiom,
! [A2: $o > set_state,B3: $o > set_state,F: ( $o > set_state ) > $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_less_o_set_state @ ( F @ B3 ) @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_326_order__le__less__subst2,axiom,
! [A2: $o > set_state,B3: $o > set_state,F: ( $o > set_state ) > set_set_state,C: set_set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_le8280034978549525370_state @ ( F @ B3 ) @ C )
=> ( ! [X: $o > set_state,Y2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_327_order__le__less__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_state,C: set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_less_set_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_328_order__le__less__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > $o > set_state,C: $o > set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_less_o_set_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le9189382018855386905_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_329_order__le__less__subst2,axiom,
! [A2: set_set_state,B3: set_set_state,F: set_set_state > set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_le8280034978549525370_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le5175021213330142598_state @ X @ Y2 )
=> ( ord_le5175021213330142598_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_330_order__le__less__subst2,axiom,
! [A2: set_state,B3: set_state,F: set_state > set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_less_set_state @ ( F @ B3 ) @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ ( F @ A2 ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_331_order__le__less__subst1,axiom,
! [A2: set_state,F: set_state > set_state,B3: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_332_order__le__less__subst1,axiom,
! [A2: set_state,F: set_set_state > set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le2494988322063910608_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_less_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_333_order__le__less__subst1,axiom,
! [A2: $o > set_state,F: set_state > $o > set_state,B3: set_state,C: set_state] :
( ( ord_le9189382018855386905_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_less_o_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_334_order__le__less__subst1,axiom,
! [A2: $o > set_state,F: set_set_state > $o > set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le9189382018855386905_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_less_o_set_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_less_o_set_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_335_order__le__less__subst1,axiom,
! [A2: set_set_state,F: set_state > set_set_state,B3: set_state,C: set_state] :
( ( ord_le5175021213330142598_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ! [X: set_state,Y2: set_state] :
( ( ord_less_set_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_336_order__le__less__subst1,axiom,
! [A2: set_set_state,F: set_set_state > set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ ( F @ B3 ) )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( ord_le8280034978549525370_state @ X @ Y2 )
=> ( ord_le8280034978549525370_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( ord_le8280034978549525370_state @ A2 @ ( F @ C ) ) ) ) ) ).
% order_le_less_subst1
thf(fact_337_order__less__le__trans,axiom,
! [X2: $o > set_state,Y: $o > set_state,Z2: $o > set_state] :
( ( ord_less_o_set_state @ X2 @ Y )
=> ( ( ord_le9189382018855386905_state @ Y @ Z2 )
=> ( ord_less_o_set_state @ X2 @ Z2 ) ) ) ).
% order_less_le_trans
thf(fact_338_order__less__le__trans,axiom,
! [X2: set_set_state,Y: set_set_state,Z2: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ( ( ord_le5175021213330142598_state @ Y @ Z2 )
=> ( ord_le8280034978549525370_state @ X2 @ Z2 ) ) ) ).
% order_less_le_trans
thf(fact_339_order__less__le__trans,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ( ( ord_le2494988322063910608_state @ Y @ Z2 )
=> ( ord_less_set_state @ X2 @ Z2 ) ) ) ).
% order_less_le_trans
thf(fact_340_order__le__less__trans,axiom,
! [X2: $o > set_state,Y: $o > set_state,Z2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ Y )
=> ( ( ord_less_o_set_state @ Y @ Z2 )
=> ( ord_less_o_set_state @ X2 @ Z2 ) ) ) ).
% order_le_less_trans
thf(fact_341_order__le__less__trans,axiom,
! [X2: set_set_state,Y: set_set_state,Z2: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ Y )
=> ( ( ord_le8280034978549525370_state @ Y @ Z2 )
=> ( ord_le8280034978549525370_state @ X2 @ Z2 ) ) ) ).
% order_le_less_trans
thf(fact_342_order__le__less__trans,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( ord_less_set_state @ Y @ Z2 )
=> ( ord_less_set_state @ X2 @ Z2 ) ) ) ).
% order_le_less_trans
thf(fact_343_order__neq__le__trans,axiom,
! [A2: $o > set_state,B3: $o > set_state] :
( ( A2 != B3 )
=> ( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ord_less_o_set_state @ A2 @ B3 ) ) ) ).
% order_neq_le_trans
thf(fact_344_order__neq__le__trans,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( A2 != B3 )
=> ( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ord_le8280034978549525370_state @ A2 @ B3 ) ) ) ).
% order_neq_le_trans
thf(fact_345_order__neq__le__trans,axiom,
! [A2: set_state,B3: set_state] :
( ( A2 != B3 )
=> ( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ord_less_set_state @ A2 @ B3 ) ) ) ).
% order_neq_le_trans
thf(fact_346_order__le__neq__trans,axiom,
! [A2: $o > set_state,B3: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( A2 != B3 )
=> ( ord_less_o_set_state @ A2 @ B3 ) ) ) ).
% order_le_neq_trans
thf(fact_347_order__le__neq__trans,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( A2 != B3 )
=> ( ord_le8280034978549525370_state @ A2 @ B3 ) ) ) ).
% order_le_neq_trans
thf(fact_348_order__le__neq__trans,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( A2 != B3 )
=> ( ord_less_set_state @ A2 @ B3 ) ) ) ).
% order_le_neq_trans
thf(fact_349_order__less__imp__le,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_less_o_set_state @ X2 @ Y )
=> ( ord_le9189382018855386905_state @ X2 @ Y ) ) ).
% order_less_imp_le
thf(fact_350_order__less__imp__le,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ( ord_le5175021213330142598_state @ X2 @ Y ) ) ).
% order_less_imp_le
thf(fact_351_order__less__imp__le,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ( ord_le2494988322063910608_state @ X2 @ Y ) ) ).
% order_less_imp_le
thf(fact_352_order__less__le,axiom,
( ord_less_o_set_state
= ( ^ [X3: $o > set_state,Y4: $o > set_state] :
( ( ord_le9189382018855386905_state @ X3 @ Y4 )
& ( X3 != Y4 ) ) ) ) ).
% order_less_le
thf(fact_353_order__less__le,axiom,
( ord_le8280034978549525370_state
= ( ^ [X3: set_set_state,Y4: set_set_state] :
( ( ord_le5175021213330142598_state @ X3 @ Y4 )
& ( X3 != Y4 ) ) ) ) ).
% order_less_le
thf(fact_354_order__less__le,axiom,
( ord_less_set_state
= ( ^ [X3: set_state,Y4: set_state] :
( ( ord_le2494988322063910608_state @ X3 @ Y4 )
& ( X3 != Y4 ) ) ) ) ).
% order_less_le
thf(fact_355_order__le__less,axiom,
( ord_le9189382018855386905_state
= ( ^ [X3: $o > set_state,Y4: $o > set_state] :
( ( ord_less_o_set_state @ X3 @ Y4 )
| ( X3 = Y4 ) ) ) ) ).
% order_le_less
thf(fact_356_order__le__less,axiom,
( ord_le5175021213330142598_state
= ( ^ [X3: set_set_state,Y4: set_set_state] :
( ( ord_le8280034978549525370_state @ X3 @ Y4 )
| ( X3 = Y4 ) ) ) ) ).
% order_le_less
thf(fact_357_order__le__less,axiom,
( ord_le2494988322063910608_state
= ( ^ [X3: set_state,Y4: set_state] :
( ( ord_less_set_state @ X3 @ Y4 )
| ( X3 = Y4 ) ) ) ) ).
% order_le_less
thf(fact_358_dual__order_Ostrict__implies__order,axiom,
! [B3: $o > set_state,A2: $o > set_state] :
( ( ord_less_o_set_state @ B3 @ A2 )
=> ( ord_le9189382018855386905_state @ B3 @ A2 ) ) ).
% dual_order.strict_implies_order
thf(fact_359_dual__order_Ostrict__implies__order,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( ord_le8280034978549525370_state @ B3 @ A2 )
=> ( ord_le5175021213330142598_state @ B3 @ A2 ) ) ).
% dual_order.strict_implies_order
thf(fact_360_dual__order_Ostrict__implies__order,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_less_set_state @ B3 @ A2 )
=> ( ord_le2494988322063910608_state @ B3 @ A2 ) ) ).
% dual_order.strict_implies_order
thf(fact_361_order_Ostrict__implies__order,axiom,
! [A2: $o > set_state,B3: $o > set_state] :
( ( ord_less_o_set_state @ A2 @ B3 )
=> ( ord_le9189382018855386905_state @ A2 @ B3 ) ) ).
% order.strict_implies_order
thf(fact_362_order_Ostrict__implies__order,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ord_le5175021213330142598_state @ A2 @ B3 ) ) ).
% order.strict_implies_order
thf(fact_363_order_Ostrict__implies__order,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ord_le2494988322063910608_state @ A2 @ B3 ) ) ).
% order.strict_implies_order
thf(fact_364_dual__order_Ostrict__iff__not,axiom,
( ord_less_o_set_state
= ( ^ [B4: $o > set_state,A4: $o > set_state] :
( ( ord_le9189382018855386905_state @ B4 @ A4 )
& ~ ( ord_le9189382018855386905_state @ A4 @ B4 ) ) ) ) ).
% dual_order.strict_iff_not
thf(fact_365_dual__order_Ostrict__iff__not,axiom,
( ord_le8280034978549525370_state
= ( ^ [B4: set_set_state,A4: set_set_state] :
( ( ord_le5175021213330142598_state @ B4 @ A4 )
& ~ ( ord_le5175021213330142598_state @ A4 @ B4 ) ) ) ) ).
% dual_order.strict_iff_not
thf(fact_366_dual__order_Ostrict__iff__not,axiom,
( ord_less_set_state
= ( ^ [B4: set_state,A4: set_state] :
( ( ord_le2494988322063910608_state @ B4 @ A4 )
& ~ ( ord_le2494988322063910608_state @ A4 @ B4 ) ) ) ) ).
% dual_order.strict_iff_not
thf(fact_367_dual__order_Ostrict__trans2,axiom,
! [B3: $o > set_state,A2: $o > set_state,C: $o > set_state] :
( ( ord_less_o_set_state @ B3 @ A2 )
=> ( ( ord_le9189382018855386905_state @ C @ B3 )
=> ( ord_less_o_set_state @ C @ A2 ) ) ) ).
% dual_order.strict_trans2
thf(fact_368_dual__order_Ostrict__trans2,axiom,
! [B3: set_set_state,A2: set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ B3 @ A2 )
=> ( ( ord_le5175021213330142598_state @ C @ B3 )
=> ( ord_le8280034978549525370_state @ C @ A2 ) ) ) ).
% dual_order.strict_trans2
thf(fact_369_dual__order_Ostrict__trans2,axiom,
! [B3: set_state,A2: set_state,C: set_state] :
( ( ord_less_set_state @ B3 @ A2 )
=> ( ( ord_le2494988322063910608_state @ C @ B3 )
=> ( ord_less_set_state @ C @ A2 ) ) ) ).
% dual_order.strict_trans2
thf(fact_370_dual__order_Ostrict__trans1,axiom,
! [B3: $o > set_state,A2: $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ B3 @ A2 )
=> ( ( ord_less_o_set_state @ C @ B3 )
=> ( ord_less_o_set_state @ C @ A2 ) ) ) ).
% dual_order.strict_trans1
thf(fact_371_dual__order_Ostrict__trans1,axiom,
! [B3: set_set_state,A2: set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ B3 @ A2 )
=> ( ( ord_le8280034978549525370_state @ C @ B3 )
=> ( ord_le8280034978549525370_state @ C @ A2 ) ) ) ).
% dual_order.strict_trans1
thf(fact_372_dual__order_Ostrict__trans1,axiom,
! [B3: set_state,A2: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ( ( ord_less_set_state @ C @ B3 )
=> ( ord_less_set_state @ C @ A2 ) ) ) ).
% dual_order.strict_trans1
thf(fact_373_dual__order_Ostrict__iff__order,axiom,
( ord_less_o_set_state
= ( ^ [B4: $o > set_state,A4: $o > set_state] :
( ( ord_le9189382018855386905_state @ B4 @ A4 )
& ( A4 != B4 ) ) ) ) ).
% dual_order.strict_iff_order
thf(fact_374_dual__order_Ostrict__iff__order,axiom,
( ord_le8280034978549525370_state
= ( ^ [B4: set_set_state,A4: set_set_state] :
( ( ord_le5175021213330142598_state @ B4 @ A4 )
& ( A4 != B4 ) ) ) ) ).
% dual_order.strict_iff_order
thf(fact_375_dual__order_Ostrict__iff__order,axiom,
( ord_less_set_state
= ( ^ [B4: set_state,A4: set_state] :
( ( ord_le2494988322063910608_state @ B4 @ A4 )
& ( A4 != B4 ) ) ) ) ).
% dual_order.strict_iff_order
thf(fact_376_dual__order_Oorder__iff__strict,axiom,
( ord_le9189382018855386905_state
= ( ^ [B4: $o > set_state,A4: $o > set_state] :
( ( ord_less_o_set_state @ B4 @ A4 )
| ( A4 = B4 ) ) ) ) ).
% dual_order.order_iff_strict
thf(fact_377_dual__order_Oorder__iff__strict,axiom,
( ord_le5175021213330142598_state
= ( ^ [B4: set_set_state,A4: set_set_state] :
( ( ord_le8280034978549525370_state @ B4 @ A4 )
| ( A4 = B4 ) ) ) ) ).
% dual_order.order_iff_strict
thf(fact_378_dual__order_Oorder__iff__strict,axiom,
( ord_le2494988322063910608_state
= ( ^ [B4: set_state,A4: set_state] :
( ( ord_less_set_state @ B4 @ A4 )
| ( A4 = B4 ) ) ) ) ).
% dual_order.order_iff_strict
thf(fact_379_order_Ostrict__iff__not,axiom,
( ord_less_o_set_state
= ( ^ [A4: $o > set_state,B4: $o > set_state] :
( ( ord_le9189382018855386905_state @ A4 @ B4 )
& ~ ( ord_le9189382018855386905_state @ B4 @ A4 ) ) ) ) ).
% order.strict_iff_not
thf(fact_380_order_Ostrict__iff__not,axiom,
( ord_le8280034978549525370_state
= ( ^ [A4: set_set_state,B4: set_set_state] :
( ( ord_le5175021213330142598_state @ A4 @ B4 )
& ~ ( ord_le5175021213330142598_state @ B4 @ A4 ) ) ) ) ).
% order.strict_iff_not
thf(fact_381_order_Ostrict__iff__not,axiom,
( ord_less_set_state
= ( ^ [A4: set_state,B4: set_state] :
( ( ord_le2494988322063910608_state @ A4 @ B4 )
& ~ ( ord_le2494988322063910608_state @ B4 @ A4 ) ) ) ) ).
% order.strict_iff_not
thf(fact_382_order_Ostrict__trans2,axiom,
! [A2: $o > set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_less_o_set_state @ A2 @ B3 )
=> ( ( ord_le9189382018855386905_state @ B3 @ C )
=> ( ord_less_o_set_state @ A2 @ C ) ) ) ).
% order.strict_trans2
thf(fact_383_order_Ostrict__trans2,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( ord_le5175021213330142598_state @ B3 @ C )
=> ( ord_le8280034978549525370_state @ A2 @ C ) ) ) ).
% order.strict_trans2
thf(fact_384_order_Ostrict__trans2,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ord_less_set_state @ A2 @ C ) ) ) ).
% order.strict_trans2
thf(fact_385_order_Ostrict__trans1,axiom,
! [A2: $o > set_state,B3: $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( ord_less_o_set_state @ B3 @ C )
=> ( ord_less_o_set_state @ A2 @ C ) ) ) ).
% order.strict_trans1
thf(fact_386_order_Ostrict__trans1,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( ord_le8280034978549525370_state @ B3 @ C )
=> ( ord_le8280034978549525370_state @ A2 @ C ) ) ) ).
% order.strict_trans1
thf(fact_387_order_Ostrict__trans1,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_less_set_state @ B3 @ C )
=> ( ord_less_set_state @ A2 @ C ) ) ) ).
% order.strict_trans1
thf(fact_388_order_Ostrict__iff__order,axiom,
( ord_less_o_set_state
= ( ^ [A4: $o > set_state,B4: $o > set_state] :
( ( ord_le9189382018855386905_state @ A4 @ B4 )
& ( A4 != B4 ) ) ) ) ).
% order.strict_iff_order
thf(fact_389_order_Ostrict__iff__order,axiom,
( ord_le8280034978549525370_state
= ( ^ [A4: set_set_state,B4: set_set_state] :
( ( ord_le5175021213330142598_state @ A4 @ B4 )
& ( A4 != B4 ) ) ) ) ).
% order.strict_iff_order
thf(fact_390_order_Ostrict__iff__order,axiom,
( ord_less_set_state
= ( ^ [A4: set_state,B4: set_state] :
( ( ord_le2494988322063910608_state @ A4 @ B4 )
& ( A4 != B4 ) ) ) ) ).
% order.strict_iff_order
thf(fact_391_order_Oorder__iff__strict,axiom,
( ord_le9189382018855386905_state
= ( ^ [A4: $o > set_state,B4: $o > set_state] :
( ( ord_less_o_set_state @ A4 @ B4 )
| ( A4 = B4 ) ) ) ) ).
% order.order_iff_strict
thf(fact_392_order_Oorder__iff__strict,axiom,
( ord_le5175021213330142598_state
= ( ^ [A4: set_set_state,B4: set_set_state] :
( ( ord_le8280034978549525370_state @ A4 @ B4 )
| ( A4 = B4 ) ) ) ) ).
% order.order_iff_strict
thf(fact_393_order_Oorder__iff__strict,axiom,
( ord_le2494988322063910608_state
= ( ^ [A4: set_state,B4: set_state] :
( ( ord_less_set_state @ A4 @ B4 )
| ( A4 = B4 ) ) ) ) ).
% order.order_iff_strict
thf(fact_394_less__le__not__le,axiom,
( ord_less_o_set_state
= ( ^ [X3: $o > set_state,Y4: $o > set_state] :
( ( ord_le9189382018855386905_state @ X3 @ Y4 )
& ~ ( ord_le9189382018855386905_state @ Y4 @ X3 ) ) ) ) ).
% less_le_not_le
thf(fact_395_less__le__not__le,axiom,
( ord_le8280034978549525370_state
= ( ^ [X3: set_set_state,Y4: set_set_state] :
( ( ord_le5175021213330142598_state @ X3 @ Y4 )
& ~ ( ord_le5175021213330142598_state @ Y4 @ X3 ) ) ) ) ).
% less_le_not_le
thf(fact_396_less__le__not__le,axiom,
( ord_less_set_state
= ( ^ [X3: set_state,Y4: set_state] :
( ( ord_le2494988322063910608_state @ X3 @ Y4 )
& ~ ( ord_le2494988322063910608_state @ Y4 @ X3 ) ) ) ) ).
% less_le_not_le
thf(fact_397_antisym__conv2,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ Y )
=> ( ( ~ ( ord_less_o_set_state @ X2 @ Y ) )
= ( X2 = Y ) ) ) ).
% antisym_conv2
thf(fact_398_antisym__conv2,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ Y )
=> ( ( ~ ( ord_le8280034978549525370_state @ X2 @ Y ) )
= ( X2 = Y ) ) ) ).
% antisym_conv2
thf(fact_399_antisym__conv2,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( ~ ( ord_less_set_state @ X2 @ Y ) )
= ( X2 = Y ) ) ) ).
% antisym_conv2
thf(fact_400_antisym__conv1,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ~ ( ord_less_o_set_state @ X2 @ Y )
=> ( ( ord_le9189382018855386905_state @ X2 @ Y )
= ( X2 = Y ) ) ) ).
% antisym_conv1
thf(fact_401_antisym__conv1,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ~ ( ord_le8280034978549525370_state @ X2 @ Y )
=> ( ( ord_le5175021213330142598_state @ X2 @ Y )
= ( X2 = Y ) ) ) ).
% antisym_conv1
thf(fact_402_antisym__conv1,axiom,
! [X2: set_state,Y: set_state] :
( ~ ( ord_less_set_state @ X2 @ Y )
=> ( ( ord_le2494988322063910608_state @ X2 @ Y )
= ( X2 = Y ) ) ) ).
% antisym_conv1
thf(fact_403_nless__le,axiom,
! [A2: $o > set_state,B3: $o > set_state] :
( ( ~ ( ord_less_o_set_state @ A2 @ B3 ) )
= ( ~ ( ord_le9189382018855386905_state @ A2 @ B3 )
| ( A2 = B3 ) ) ) ).
% nless_le
thf(fact_404_nless__le,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ~ ( ord_le8280034978549525370_state @ A2 @ B3 ) )
= ( ~ ( ord_le5175021213330142598_state @ A2 @ B3 )
| ( A2 = B3 ) ) ) ).
% nless_le
thf(fact_405_nless__le,axiom,
! [A2: set_state,B3: set_state] :
( ( ~ ( ord_less_set_state @ A2 @ B3 ) )
= ( ~ ( ord_le2494988322063910608_state @ A2 @ B3 )
| ( A2 = B3 ) ) ) ).
% nless_le
thf(fact_406_leD,axiom,
! [Y: $o > set_state,X2: $o > set_state] :
( ( ord_le9189382018855386905_state @ Y @ X2 )
=> ~ ( ord_less_o_set_state @ X2 @ Y ) ) ).
% leD
thf(fact_407_leD,axiom,
! [Y: set_set_state,X2: set_set_state] :
( ( ord_le5175021213330142598_state @ Y @ X2 )
=> ~ ( ord_le8280034978549525370_state @ X2 @ Y ) ) ).
% leD
thf(fact_408_leD,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_le2494988322063910608_state @ Y @ X2 )
=> ~ ( ord_less_set_state @ X2 @ Y ) ) ).
% leD
thf(fact_409_subset__iff__psubset__eq,axiom,
( ord_le5175021213330142598_state
= ( ^ [A3: set_set_state,B2: set_set_state] :
( ( ord_le8280034978549525370_state @ A3 @ B2 )
| ( A3 = B2 ) ) ) ) ).
% subset_iff_psubset_eq
thf(fact_410_subset__iff__psubset__eq,axiom,
( ord_le2494988322063910608_state
= ( ^ [A3: set_state,B2: set_state] :
( ( ord_less_set_state @ A3 @ B2 )
| ( A3 = B2 ) ) ) ) ).
% subset_iff_psubset_eq
thf(fact_411_subset__psubset__trans,axiom,
! [A: set_set_state,B: set_set_state,C2: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ B )
=> ( ( ord_le8280034978549525370_state @ B @ C2 )
=> ( ord_le8280034978549525370_state @ A @ C2 ) ) ) ).
% subset_psubset_trans
thf(fact_412_subset__psubset__trans,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( ord_less_set_state @ B @ C2 )
=> ( ord_less_set_state @ A @ C2 ) ) ) ).
% subset_psubset_trans
thf(fact_413_subset__not__subset__eq,axiom,
( ord_le8280034978549525370_state
= ( ^ [A3: set_set_state,B2: set_set_state] :
( ( ord_le5175021213330142598_state @ A3 @ B2 )
& ~ ( ord_le5175021213330142598_state @ B2 @ A3 ) ) ) ) ).
% subset_not_subset_eq
thf(fact_414_subset__not__subset__eq,axiom,
( ord_less_set_state
= ( ^ [A3: set_state,B2: set_state] :
( ( ord_le2494988322063910608_state @ A3 @ B2 )
& ~ ( ord_le2494988322063910608_state @ B2 @ A3 ) ) ) ) ).
% subset_not_subset_eq
thf(fact_415_psubset__subset__trans,axiom,
! [A: set_set_state,B: set_set_state,C2: set_set_state] :
( ( ord_le8280034978549525370_state @ A @ B )
=> ( ( ord_le5175021213330142598_state @ B @ C2 )
=> ( ord_le8280034978549525370_state @ A @ C2 ) ) ) ).
% psubset_subset_trans
thf(fact_416_psubset__subset__trans,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( ord_less_set_state @ A @ B )
=> ( ( ord_le2494988322063910608_state @ B @ C2 )
=> ( ord_less_set_state @ A @ C2 ) ) ) ).
% psubset_subset_trans
thf(fact_417_psubset__imp__subset,axiom,
! [A: set_set_state,B: set_set_state] :
( ( ord_le8280034978549525370_state @ A @ B )
=> ( ord_le5175021213330142598_state @ A @ B ) ) ).
% psubset_imp_subset
thf(fact_418_psubset__imp__subset,axiom,
! [A: set_state,B: set_state] :
( ( ord_less_set_state @ A @ B )
=> ( ord_le2494988322063910608_state @ A @ B ) ) ).
% psubset_imp_subset
thf(fact_419_psubset__eq,axiom,
( ord_le8280034978549525370_state
= ( ^ [A3: set_set_state,B2: set_set_state] :
( ( ord_le5175021213330142598_state @ A3 @ B2 )
& ( A3 != B2 ) ) ) ) ).
% psubset_eq
thf(fact_420_psubset__eq,axiom,
( ord_less_set_state
= ( ^ [A3: set_state,B2: set_state] :
( ( ord_le2494988322063910608_state @ A3 @ B2 )
& ( A3 != B2 ) ) ) ) ).
% psubset_eq
thf(fact_421_psubsetE,axiom,
! [A: set_set_state,B: set_set_state] :
( ( ord_le8280034978549525370_state @ A @ B )
=> ~ ( ( ord_le5175021213330142598_state @ A @ B )
=> ( ord_le5175021213330142598_state @ B @ A ) ) ) ).
% psubsetE
thf(fact_422_psubsetE,axiom,
! [A: set_state,B: set_state] :
( ( ord_less_set_state @ A @ B )
=> ~ ( ( ord_le2494988322063910608_state @ A @ B )
=> ( ord_le2494988322063910608_state @ B @ A ) ) ) ).
% psubsetE
thf(fact_423_less__fun__def,axiom,
( ord_less_o_set_state
= ( ^ [F2: $o > set_state,G: $o > set_state] :
( ( ord_le9189382018855386905_state @ F2 @ G )
& ~ ( ord_le9189382018855386905_state @ G @ F2 ) ) ) ) ).
% less_fun_def
thf(fact_424_subset__UNIV,axiom,
! [A: set_set_state] : ( ord_le5175021213330142598_state @ A @ top_to5262587396890829782_state ) ).
% subset_UNIV
thf(fact_425_subset__UNIV,axiom,
! [A: set_state] : ( ord_le2494988322063910608_state @ A @ top_top_set_state ) ).
% subset_UNIV
thf(fact_426_compl__less__compl__iff,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le8280034978549525370_state @ ( uminus4035512285888117871_state @ X2 ) @ ( uminus4035512285888117871_state @ Y ) )
= ( ord_le8280034978549525370_state @ Y @ X2 ) ) ).
% compl_less_compl_iff
thf(fact_427_compl__less__compl__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_less_set_state @ ( uminus472742206872269241_state @ X2 ) @ ( uminus472742206872269241_state @ Y ) )
= ( ord_less_set_state @ Y @ X2 ) ) ).
% compl_less_compl_iff
thf(fact_428_compl__le__compl__iff,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_le9189382018855386905_state @ ( uminus4730887800166984048_state @ X2 ) @ ( uminus4730887800166984048_state @ Y ) )
= ( ord_le9189382018855386905_state @ Y @ X2 ) ) ).
% compl_le_compl_iff
thf(fact_429_compl__le__compl__iff,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le5175021213330142598_state @ ( uminus4035512285888117871_state @ X2 ) @ ( uminus4035512285888117871_state @ Y ) )
= ( ord_le5175021213330142598_state @ Y @ X2 ) ) ).
% compl_le_compl_iff
thf(fact_430_compl__le__compl__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ X2 ) @ ( uminus472742206872269241_state @ Y ) )
= ( ord_le2494988322063910608_state @ Y @ X2 ) ) ).
% compl_le_compl_iff
thf(fact_431_boolean__algebra__class_Oboolean__algebra_Odouble__compl,axiom,
! [X2: set_state] :
( ( uminus472742206872269241_state @ ( uminus472742206872269241_state @ X2 ) )
= X2 ) ).
% boolean_algebra_class.boolean_algebra.double_compl
thf(fact_432_boolean__algebra__class_Oboolean__algebra_Ocompl__eq__compl__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( ( uminus472742206872269241_state @ X2 )
= ( uminus472742206872269241_state @ Y ) )
= ( X2 = Y ) ) ).
% boolean_algebra_class.boolean_algebra.compl_eq_compl_iff
thf(fact_433_iso__tuple__UNIV__I,axiom,
! [X2: set_set_state] : ( member_set_set_state @ X2 @ top_to3598970937283095436_state ) ).
% iso_tuple_UNIV_I
thf(fact_434_iso__tuple__UNIV__I,axiom,
! [X2: set_state] : ( member_set_state @ X2 @ top_to5262587396890829782_state ) ).
% iso_tuple_UNIV_I
thf(fact_435_iso__tuple__UNIV__I,axiom,
! [X2: state] : ( member_state @ X2 @ top_top_set_state ) ).
% iso_tuple_UNIV_I
thf(fact_436_psubset__trans,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( ord_less_set_state @ A @ B )
=> ( ( ord_less_set_state @ B @ C2 )
=> ( ord_less_set_state @ A @ C2 ) ) ) ).
% psubset_trans
thf(fact_437_psubset__trans,axiom,
! [A: set_set_state,B: set_set_state,C2: set_set_state] :
( ( ord_le8280034978549525370_state @ A @ B )
=> ( ( ord_le8280034978549525370_state @ B @ C2 )
=> ( ord_le8280034978549525370_state @ A @ C2 ) ) ) ).
% psubset_trans
thf(fact_438_psubsetD,axiom,
! [A: set_set_set_state,B: set_set_set_state,C: set_set_state] :
( ( ord_le6814633228373517104_state @ A @ B )
=> ( ( member_set_set_state @ C @ A )
=> ( member_set_set_state @ C @ B ) ) ) ).
% psubsetD
thf(fact_439_psubsetD,axiom,
! [A: set_set_state,B: set_set_state,C: set_state] :
( ( ord_le8280034978549525370_state @ A @ B )
=> ( ( member_set_state @ C @ A )
=> ( member_set_state @ C @ B ) ) ) ).
% psubsetD
thf(fact_440_psubsetD,axiom,
! [A: set_state,B: set_state,C: state] :
( ( ord_less_set_state @ A @ B )
=> ( ( member_state @ C @ A )
=> ( member_state @ C @ B ) ) ) ).
% psubsetD
thf(fact_441_top__set__def,axiom,
( top_top_set_state
= ( collect_state @ top_top_state_o ) ) ).
% top_set_def
thf(fact_442_top__set__def,axiom,
( top_to5262587396890829782_state
= ( collect_set_state @ top_top_set_state_o ) ) ).
% top_set_def
thf(fact_443_compl__mono,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ Y )
=> ( ord_le9189382018855386905_state @ ( uminus4730887800166984048_state @ Y ) @ ( uminus4730887800166984048_state @ X2 ) ) ) ).
% compl_mono
thf(fact_444_compl__mono,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ Y )
=> ( ord_le5175021213330142598_state @ ( uminus4035512285888117871_state @ Y ) @ ( uminus4035512285888117871_state @ X2 ) ) ) ).
% compl_mono
thf(fact_445_compl__mono,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ Y ) @ ( uminus472742206872269241_state @ X2 ) ) ) ).
% compl_mono
thf(fact_446_compl__le__swap1,axiom,
! [Y: $o > set_state,X2: $o > set_state] :
( ( ord_le9189382018855386905_state @ Y @ ( uminus4730887800166984048_state @ X2 ) )
=> ( ord_le9189382018855386905_state @ X2 @ ( uminus4730887800166984048_state @ Y ) ) ) ).
% compl_le_swap1
thf(fact_447_compl__le__swap1,axiom,
! [Y: set_set_state,X2: set_set_state] :
( ( ord_le5175021213330142598_state @ Y @ ( uminus4035512285888117871_state @ X2 ) )
=> ( ord_le5175021213330142598_state @ X2 @ ( uminus4035512285888117871_state @ Y ) ) ) ).
% compl_le_swap1
thf(fact_448_compl__le__swap1,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_le2494988322063910608_state @ Y @ ( uminus472742206872269241_state @ X2 ) )
=> ( ord_le2494988322063910608_state @ X2 @ ( uminus472742206872269241_state @ Y ) ) ) ).
% compl_le_swap1
thf(fact_449_compl__le__swap2,axiom,
! [Y: $o > set_state,X2: $o > set_state] :
( ( ord_le9189382018855386905_state @ ( uminus4730887800166984048_state @ Y ) @ X2 )
=> ( ord_le9189382018855386905_state @ ( uminus4730887800166984048_state @ X2 ) @ Y ) ) ).
% compl_le_swap2
thf(fact_450_compl__le__swap2,axiom,
! [Y: set_set_state,X2: set_set_state] :
( ( ord_le5175021213330142598_state @ ( uminus4035512285888117871_state @ Y ) @ X2 )
=> ( ord_le5175021213330142598_state @ ( uminus4035512285888117871_state @ X2 ) @ Y ) ) ).
% compl_le_swap2
thf(fact_451_compl__le__swap2,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ Y ) @ X2 )
=> ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ X2 ) @ Y ) ) ).
% compl_le_swap2
thf(fact_452_compl__less__swap2,axiom,
! [Y: set_set_state,X2: set_set_state] :
( ( ord_le8280034978549525370_state @ ( uminus4035512285888117871_state @ Y ) @ X2 )
=> ( ord_le8280034978549525370_state @ ( uminus4035512285888117871_state @ X2 ) @ Y ) ) ).
% compl_less_swap2
thf(fact_453_compl__less__swap2,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_less_set_state @ ( uminus472742206872269241_state @ Y ) @ X2 )
=> ( ord_less_set_state @ ( uminus472742206872269241_state @ X2 ) @ Y ) ) ).
% compl_less_swap2
thf(fact_454_compl__less__swap1,axiom,
! [Y: set_set_state,X2: set_set_state] :
( ( ord_le8280034978549525370_state @ Y @ ( uminus4035512285888117871_state @ X2 ) )
=> ( ord_le8280034978549525370_state @ X2 @ ( uminus4035512285888117871_state @ Y ) ) ) ).
% compl_less_swap1
thf(fact_455_compl__less__swap1,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_less_set_state @ Y @ ( uminus472742206872269241_state @ X2 ) )
=> ( ord_less_set_state @ X2 @ ( uminus472742206872269241_state @ Y ) ) ) ).
% compl_less_swap1
thf(fact_456_top_Oordering__top__axioms,axiom,
ordering_top_state_o @ ord_less_eq_state_o @ ord_less_state_o @ top_top_state_o ).
% top.ordering_top_axioms
thf(fact_457_top_Oordering__top__axioms,axiom,
orderi4116547514405938474_state @ ord_le9189382018855386905_state @ ord_less_o_set_state @ top_top_o_set_state ).
% top.ordering_top_axioms
thf(fact_458_top_Oordering__top__axioms,axiom,
orderi6282941313354935349_state @ ord_le5175021213330142598_state @ ord_le8280034978549525370_state @ top_to5262587396890829782_state ).
% top.ordering_top_axioms
thf(fact_459_top_Oordering__top__axioms,axiom,
orderi2162033302644881791_state @ ord_le2494988322063910608_state @ ord_less_set_state @ top_top_set_state ).
% top.ordering_top_axioms
thf(fact_460_top1I,axiom,
! [X2: state] : ( top_top_state_o @ X2 ) ).
% top1I
thf(fact_461_greaterThanLessThan__iff,axiom,
! [I: set_set_state,L: set_set_state,U: set_set_state] :
( ( member_set_set_state @ I @ ( set_or4346910941253671034_state @ L @ U ) )
= ( ( ord_le8280034978549525370_state @ L @ I )
& ( ord_le8280034978549525370_state @ I @ U ) ) ) ).
% greaterThanLessThan_iff
thf(fact_462_greaterThanLessThan__iff,axiom,
! [I: set_state,L: set_state,U: set_state] :
( ( member_set_state @ I @ ( set_or421293776985356740_state @ L @ U ) )
= ( ( ord_less_set_state @ L @ I )
& ( ord_less_set_state @ I @ U ) ) ) ).
% greaterThanLessThan_iff
thf(fact_463_ordering__top_Oextremum__uniqueI,axiom,
! [Less_eq2: set_state > set_state > $o,Less: set_state > set_state > $o,Top: set_state,A2: set_state] :
( ( orderi2162033302644881791_state @ Less_eq2 @ Less @ Top )
=> ( ( Less_eq2 @ Top @ A2 )
=> ( A2 = Top ) ) ) ).
% ordering_top.extremum_uniqueI
thf(fact_464_ordering__top_Onot__eq__extremum,axiom,
! [Less_eq2: set_state > set_state > $o,Less: set_state > set_state > $o,Top: set_state,A2: set_state] :
( ( orderi2162033302644881791_state @ Less_eq2 @ Less @ Top )
=> ( ( A2 != Top )
= ( Less @ A2 @ Top ) ) ) ).
% ordering_top.not_eq_extremum
thf(fact_465_ordering__top_Oextremum__unique,axiom,
! [Less_eq2: set_state > set_state > $o,Less: set_state > set_state > $o,Top: set_state,A2: set_state] :
( ( orderi2162033302644881791_state @ Less_eq2 @ Less @ Top )
=> ( ( Less_eq2 @ Top @ A2 )
= ( A2 = Top ) ) ) ).
% ordering_top.extremum_unique
thf(fact_466_ordering__top_Oextremum__strict,axiom,
! [Less_eq2: set_state > set_state > $o,Less: set_state > set_state > $o,Top: set_state,A2: set_state] :
( ( orderi2162033302644881791_state @ Less_eq2 @ Less @ Top )
=> ~ ( Less @ Top @ A2 ) ) ).
% ordering_top.extremum_strict
thf(fact_467_ordering__top_Oextremum,axiom,
! [Less_eq2: set_state > set_state > $o,Less: set_state > set_state > $o,Top: set_state,A2: set_state] :
( ( orderi2162033302644881791_state @ Less_eq2 @ Less @ Top )
=> ( Less_eq2 @ A2 @ Top ) ) ).
% ordering_top.extremum
thf(fact_468_top__empty__eq,axiom,
( top_to8638843179453837305tate_o
= ( ^ [X3: set_set_state] : ( member_set_set_state @ X3 @ top_to3598970937283095436_state ) ) ) ).
% top_empty_eq
thf(fact_469_top__empty__eq,axiom,
( top_top_set_state_o
= ( ^ [X3: set_state] : ( member_set_state @ X3 @ top_to5262587396890829782_state ) ) ) ).
% top_empty_eq
thf(fact_470_top__empty__eq,axiom,
( top_top_state_o
= ( ^ [X3: state] : ( member_state @ X3 @ top_top_set_state ) ) ) ).
% top_empty_eq
thf(fact_471_top__conj_I2_J,axiom,
! [P: $o,X2: state] :
( ( P
& ( top_top_state_o @ X2 ) )
= P ) ).
% top_conj(2)
thf(fact_472_top__conj_I1_J,axiom,
! [X2: state,P: $o] :
( ( ( top_top_state_o @ X2 )
& P )
= P ) ).
% top_conj(1)
thf(fact_473_empty__iff,axiom,
! [C: set_set_state] :
~ ( member_set_set_state @ C @ bot_bo7389043141884672880_state ) ).
% empty_iff
thf(fact_474_empty__iff,axiom,
! [C: set_state] :
~ ( member_set_state @ C @ bot_bo2271482359692755898_state ) ).
% empty_iff
thf(fact_475_empty__iff,axiom,
! [C: state] :
~ ( member_state @ C @ bot_bot_set_state ) ).
% empty_iff
thf(fact_476_all__not__in__conv,axiom,
! [A: set_set_set_state] :
( ( ! [X3: set_set_state] :
~ ( member_set_set_state @ X3 @ A ) )
= ( A = bot_bo7389043141884672880_state ) ) ).
% all_not_in_conv
thf(fact_477_all__not__in__conv,axiom,
! [A: set_set_state] :
( ( ! [X3: set_state] :
~ ( member_set_state @ X3 @ A ) )
= ( A = bot_bo2271482359692755898_state ) ) ).
% all_not_in_conv
thf(fact_478_all__not__in__conv,axiom,
! [A: set_state] :
( ( ! [X3: state] :
~ ( member_state @ X3 @ A ) )
= ( A = bot_bot_set_state ) ) ).
% all_not_in_conv
thf(fact_479_Collect__empty__eq,axiom,
! [P: state > $o] :
( ( ( collect_state @ P )
= bot_bot_set_state )
= ( ! [X3: state] :
~ ( P @ X3 ) ) ) ).
% Collect_empty_eq
thf(fact_480_Collect__empty__eq,axiom,
! [P: set_state > $o] :
( ( ( collect_set_state @ P )
= bot_bo2271482359692755898_state )
= ( ! [X3: set_state] :
~ ( P @ X3 ) ) ) ).
% Collect_empty_eq
thf(fact_481_empty__Collect__eq,axiom,
! [P: state > $o] :
( ( bot_bot_set_state
= ( collect_state @ P ) )
= ( ! [X3: state] :
~ ( P @ X3 ) ) ) ).
% empty_Collect_eq
thf(fact_482_empty__Collect__eq,axiom,
! [P: set_state > $o] :
( ( bot_bo2271482359692755898_state
= ( collect_set_state @ P ) )
= ( ! [X3: set_state] :
~ ( P @ X3 ) ) ) ).
% empty_Collect_eq
thf(fact_483_sup_Oidem,axiom,
! [A2: set_state] :
( ( sup_sup_set_state @ A2 @ A2 )
= A2 ) ).
% sup.idem
thf(fact_484_sup_Oidem,axiom,
! [A2: set_set_state] :
( ( sup_su4188871578264421970_state @ A2 @ A2 )
= A2 ) ).
% sup.idem
thf(fact_485_sup_Oidem,axiom,
! [A2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ A2 @ A2 )
= A2 ) ).
% sup.idem
thf(fact_486_sup__idem,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ X2 @ X2 )
= X2 ) ).
% sup_idem
thf(fact_487_sup__idem,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ X2 )
= X2 ) ).
% sup_idem
thf(fact_488_sup__idem,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ X2 )
= X2 ) ).
% sup_idem
thf(fact_489_sup_Oleft__idem,axiom,
! [A2: set_state,B3: set_state] :
( ( sup_sup_set_state @ A2 @ ( sup_sup_set_state @ A2 @ B3 ) )
= ( sup_sup_set_state @ A2 @ B3 ) ) ).
% sup.left_idem
thf(fact_490_sup_Oleft__idem,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( sup_su4188871578264421970_state @ A2 @ ( sup_su4188871578264421970_state @ A2 @ B3 ) )
= ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ).
% sup.left_idem
thf(fact_491_sup_Oleft__idem,axiom,
! [A2: state > state > $o,B3: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ A2 @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) )
= ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ).
% sup.left_idem
thf(fact_492_sup__left__idem,axiom,
! [X2: set_state,Y: set_state] :
( ( sup_sup_set_state @ X2 @ ( sup_sup_set_state @ X2 @ Y ) )
= ( sup_sup_set_state @ X2 @ Y ) ) ).
% sup_left_idem
thf(fact_493_sup__left__idem,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ ( sup_su4188871578264421970_state @ X2 @ Y ) )
= ( sup_su4188871578264421970_state @ X2 @ Y ) ) ).
% sup_left_idem
thf(fact_494_sup__left__idem,axiom,
! [X2: state > state > $o,Y: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) )
= ( sup_su7525921995284788454tate_o @ X2 @ Y ) ) ).
% sup_left_idem
thf(fact_495_sup_Oright__idem,axiom,
! [A2: set_state,B3: set_state] :
( ( sup_sup_set_state @ ( sup_sup_set_state @ A2 @ B3 ) @ B3 )
= ( sup_sup_set_state @ A2 @ B3 ) ) ).
% sup.right_idem
thf(fact_496_sup_Oright__idem,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( sup_su4188871578264421970_state @ ( sup_su4188871578264421970_state @ A2 @ B3 ) @ B3 )
= ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ).
% sup.right_idem
thf(fact_497_sup_Oright__idem,axiom,
! [A2: state > state > $o,B3: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) @ B3 )
= ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ).
% sup.right_idem
thf(fact_498_sup__apply,axiom,
( sup_su7525921995284788454tate_o
= ( ^ [F2: state > state > $o,G: state > state > $o,X3: state] : ( sup_sup_state_o @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% sup_apply
thf(fact_499_UnCI,axiom,
! [C: set_set_state,B: set_set_set_state,A: set_set_set_state] :
( ( ~ ( member_set_set_state @ C @ B )
=> ( member_set_set_state @ C @ A ) )
=> ( member_set_set_state @ C @ ( sup_su3277220503338409480_state @ A @ B ) ) ) ).
% UnCI
thf(fact_500_UnCI,axiom,
! [C: set_state,B: set_set_state,A: set_set_state] :
( ( ~ ( member_set_state @ C @ B )
=> ( member_set_state @ C @ A ) )
=> ( member_set_state @ C @ ( sup_su4188871578264421970_state @ A @ B ) ) ) ).
% UnCI
thf(fact_501_UnCI,axiom,
! [C: state,B: set_state,A: set_state] :
( ( ~ ( member_state @ C @ B )
=> ( member_state @ C @ A ) )
=> ( member_state @ C @ ( sup_sup_set_state @ A @ B ) ) ) ).
% UnCI
thf(fact_502_Un__iff,axiom,
! [C: set_set_state,A: set_set_set_state,B: set_set_set_state] :
( ( member_set_set_state @ C @ ( sup_su3277220503338409480_state @ A @ B ) )
= ( ( member_set_set_state @ C @ A )
| ( member_set_set_state @ C @ B ) ) ) ).
% Un_iff
thf(fact_503_Un__iff,axiom,
! [C: set_state,A: set_set_state,B: set_set_state] :
( ( member_set_state @ C @ ( sup_su4188871578264421970_state @ A @ B ) )
= ( ( member_set_state @ C @ A )
| ( member_set_state @ C @ B ) ) ) ).
% Un_iff
thf(fact_504_Un__iff,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( sup_sup_set_state @ A @ B ) )
= ( ( member_state @ C @ A )
| ( member_state @ C @ B ) ) ) ).
% Un_iff
thf(fact_505_le__sup__iff,axiom,
! [X2: state > state > $o,Y: state > state > $o,Z2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) @ Z2 )
= ( ( ord_le4344933087531911346tate_o @ X2 @ Z2 )
& ( ord_le4344933087531911346tate_o @ Y @ Z2 ) ) ) ).
% le_sup_iff
thf(fact_506_le__sup__iff,axiom,
! [X2: $o > set_state,Y: $o > set_state,Z2: $o > set_state] :
( ( ord_le9189382018855386905_state @ ( sup_sup_o_set_state @ X2 @ Y ) @ Z2 )
= ( ( ord_le9189382018855386905_state @ X2 @ Z2 )
& ( ord_le9189382018855386905_state @ Y @ Z2 ) ) ) ).
% le_sup_iff
thf(fact_507_le__sup__iff,axiom,
! [X2: set_set_state,Y: set_set_state,Z2: set_set_state] :
( ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ X2 @ Y ) @ Z2 )
= ( ( ord_le5175021213330142598_state @ X2 @ Z2 )
& ( ord_le5175021213330142598_state @ Y @ Z2 ) ) ) ).
% le_sup_iff
thf(fact_508_le__sup__iff,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ X2 @ Y ) @ Z2 )
= ( ( ord_le2494988322063910608_state @ X2 @ Z2 )
& ( ord_le2494988322063910608_state @ Y @ Z2 ) ) ) ).
% le_sup_iff
thf(fact_509_sup_Obounded__iff,axiom,
! [B3: state > state > $o,C: state > state > $o,A2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ ( sup_su7525921995284788454tate_o @ B3 @ C ) @ A2 )
= ( ( ord_le4344933087531911346tate_o @ B3 @ A2 )
& ( ord_le4344933087531911346tate_o @ C @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_510_sup_Obounded__iff,axiom,
! [B3: $o > set_state,C: $o > set_state,A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ ( sup_sup_o_set_state @ B3 @ C ) @ A2 )
= ( ( ord_le9189382018855386905_state @ B3 @ A2 )
& ( ord_le9189382018855386905_state @ C @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_511_sup_Obounded__iff,axiom,
! [B3: set_set_state,C: set_set_state,A2: set_set_state] :
( ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ B3 @ C ) @ A2 )
= ( ( ord_le5175021213330142598_state @ B3 @ A2 )
& ( ord_le5175021213330142598_state @ C @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_512_sup_Obounded__iff,axiom,
! [B3: set_state,C: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B3 @ C ) @ A2 )
= ( ( ord_le2494988322063910608_state @ B3 @ A2 )
& ( ord_le2494988322063910608_state @ C @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_513_subset__empty,axiom,
! [A: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ bot_bo2271482359692755898_state )
= ( A = bot_bo2271482359692755898_state ) ) ).
% subset_empty
thf(fact_514_subset__empty,axiom,
! [A: set_state] :
( ( ord_le2494988322063910608_state @ A @ bot_bot_set_state )
= ( A = bot_bot_set_state ) ) ).
% subset_empty
thf(fact_515_empty__subsetI,axiom,
! [A: set_set_state] : ( ord_le5175021213330142598_state @ bot_bo2271482359692755898_state @ A ) ).
% empty_subsetI
thf(fact_516_empty__subsetI,axiom,
! [A: set_state] : ( ord_le2494988322063910608_state @ bot_bot_set_state @ A ) ).
% empty_subsetI
thf(fact_517_sup__bot__left,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ bot_bo3298213311409307006tate_o @ X2 )
= X2 ) ).
% sup_bot_left
thf(fact_518_sup__bot__left,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ bot_bot_set_state @ X2 )
= X2 ) ).
% sup_bot_left
thf(fact_519_sup__bot__left,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ bot_bo2271482359692755898_state @ X2 )
= X2 ) ).
% sup_bot_left
thf(fact_520_sup__bot__right,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ bot_bo3298213311409307006tate_o )
= X2 ) ).
% sup_bot_right
thf(fact_521_sup__bot__right,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ X2 @ bot_bot_set_state )
= X2 ) ).
% sup_bot_right
thf(fact_522_sup__bot__right,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ bot_bo2271482359692755898_state )
= X2 ) ).
% sup_bot_right
thf(fact_523_bot__eq__sup__iff,axiom,
! [X2: state > state > $o,Y: state > state > $o] :
( ( bot_bo3298213311409307006tate_o
= ( sup_su7525921995284788454tate_o @ X2 @ Y ) )
= ( ( X2 = bot_bo3298213311409307006tate_o )
& ( Y = bot_bo3298213311409307006tate_o ) ) ) ).
% bot_eq_sup_iff
thf(fact_524_bot__eq__sup__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( bot_bot_set_state
= ( sup_sup_set_state @ X2 @ Y ) )
= ( ( X2 = bot_bot_set_state )
& ( Y = bot_bot_set_state ) ) ) ).
% bot_eq_sup_iff
thf(fact_525_bot__eq__sup__iff,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( bot_bo2271482359692755898_state
= ( sup_su4188871578264421970_state @ X2 @ Y ) )
= ( ( X2 = bot_bo2271482359692755898_state )
& ( Y = bot_bo2271482359692755898_state ) ) ) ).
% bot_eq_sup_iff
thf(fact_526_sup__eq__bot__iff,axiom,
! [X2: state > state > $o,Y: state > state > $o] :
( ( ( sup_su7525921995284788454tate_o @ X2 @ Y )
= bot_bo3298213311409307006tate_o )
= ( ( X2 = bot_bo3298213311409307006tate_o )
& ( Y = bot_bo3298213311409307006tate_o ) ) ) ).
% sup_eq_bot_iff
thf(fact_527_sup__eq__bot__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( ( sup_sup_set_state @ X2 @ Y )
= bot_bot_set_state )
= ( ( X2 = bot_bot_set_state )
& ( Y = bot_bot_set_state ) ) ) ).
% sup_eq_bot_iff
thf(fact_528_sup__eq__bot__iff,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ( sup_su4188871578264421970_state @ X2 @ Y )
= bot_bo2271482359692755898_state )
= ( ( X2 = bot_bo2271482359692755898_state )
& ( Y = bot_bo2271482359692755898_state ) ) ) ).
% sup_eq_bot_iff
thf(fact_529_sup__bot_Oeq__neutr__iff,axiom,
! [A2: state > state > $o,B3: state > state > $o] :
( ( ( sup_su7525921995284788454tate_o @ A2 @ B3 )
= bot_bo3298213311409307006tate_o )
= ( ( A2 = bot_bo3298213311409307006tate_o )
& ( B3 = bot_bo3298213311409307006tate_o ) ) ) ).
% sup_bot.eq_neutr_iff
thf(fact_530_sup__bot_Oeq__neutr__iff,axiom,
! [A2: set_state,B3: set_state] :
( ( ( sup_sup_set_state @ A2 @ B3 )
= bot_bot_set_state )
= ( ( A2 = bot_bot_set_state )
& ( B3 = bot_bot_set_state ) ) ) ).
% sup_bot.eq_neutr_iff
thf(fact_531_sup__bot_Oeq__neutr__iff,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ( sup_su4188871578264421970_state @ A2 @ B3 )
= bot_bo2271482359692755898_state )
= ( ( A2 = bot_bo2271482359692755898_state )
& ( B3 = bot_bo2271482359692755898_state ) ) ) ).
% sup_bot.eq_neutr_iff
thf(fact_532_sup__bot_Oleft__neutral,axiom,
! [A2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ bot_bo3298213311409307006tate_o @ A2 )
= A2 ) ).
% sup_bot.left_neutral
thf(fact_533_sup__bot_Oleft__neutral,axiom,
! [A2: set_state] :
( ( sup_sup_set_state @ bot_bot_set_state @ A2 )
= A2 ) ).
% sup_bot.left_neutral
thf(fact_534_sup__bot_Oleft__neutral,axiom,
! [A2: set_set_state] :
( ( sup_su4188871578264421970_state @ bot_bo2271482359692755898_state @ A2 )
= A2 ) ).
% sup_bot.left_neutral
thf(fact_535_sup__bot_Oneutr__eq__iff,axiom,
! [A2: state > state > $o,B3: state > state > $o] :
( ( bot_bo3298213311409307006tate_o
= ( sup_su7525921995284788454tate_o @ A2 @ B3 ) )
= ( ( A2 = bot_bo3298213311409307006tate_o )
& ( B3 = bot_bo3298213311409307006tate_o ) ) ) ).
% sup_bot.neutr_eq_iff
thf(fact_536_sup__bot_Oneutr__eq__iff,axiom,
! [A2: set_state,B3: set_state] :
( ( bot_bot_set_state
= ( sup_sup_set_state @ A2 @ B3 ) )
= ( ( A2 = bot_bot_set_state )
& ( B3 = bot_bot_set_state ) ) ) ).
% sup_bot.neutr_eq_iff
thf(fact_537_sup__bot_Oneutr__eq__iff,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( bot_bo2271482359692755898_state
= ( sup_su4188871578264421970_state @ A2 @ B3 ) )
= ( ( A2 = bot_bo2271482359692755898_state )
& ( B3 = bot_bo2271482359692755898_state ) ) ) ).
% sup_bot.neutr_eq_iff
thf(fact_538_sup__bot_Oright__neutral,axiom,
! [A2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ A2 @ bot_bo3298213311409307006tate_o )
= A2 ) ).
% sup_bot.right_neutral
thf(fact_539_sup__bot_Oright__neutral,axiom,
! [A2: set_state] :
( ( sup_sup_set_state @ A2 @ bot_bot_set_state )
= A2 ) ).
% sup_bot.right_neutral
thf(fact_540_sup__bot_Oright__neutral,axiom,
! [A2: set_set_state] :
( ( sup_su4188871578264421970_state @ A2 @ bot_bo2271482359692755898_state )
= A2 ) ).
% sup_bot.right_neutral
thf(fact_541_boolean__algebra_Odisj__one__right,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ top_to5868225466921797218tate_o )
= top_to5868225466921797218tate_o ) ).
% boolean_algebra.disj_one_right
thf(fact_542_boolean__algebra_Odisj__one__right,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ X2 @ top_top_set_state )
= top_top_set_state ) ).
% boolean_algebra.disj_one_right
thf(fact_543_boolean__algebra_Odisj__one__right,axiom,
! [X2: state > $o] :
( ( sup_sup_state_o @ X2 @ top_top_state_o )
= top_top_state_o ) ).
% boolean_algebra.disj_one_right
thf(fact_544_boolean__algebra_Odisj__one__right,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ top_to5262587396890829782_state )
= top_to5262587396890829782_state ) ).
% boolean_algebra.disj_one_right
thf(fact_545_boolean__algebra_Odisj__one__left,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ top_to5868225466921797218tate_o @ X2 )
= top_to5868225466921797218tate_o ) ).
% boolean_algebra.disj_one_left
thf(fact_546_boolean__algebra_Odisj__one__left,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ top_top_set_state @ X2 )
= top_top_set_state ) ).
% boolean_algebra.disj_one_left
thf(fact_547_boolean__algebra_Odisj__one__left,axiom,
! [X2: state > $o] :
( ( sup_sup_state_o @ top_top_state_o @ X2 )
= top_top_state_o ) ).
% boolean_algebra.disj_one_left
thf(fact_548_boolean__algebra_Odisj__one__left,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ top_to5262587396890829782_state @ X2 )
= top_to5262587396890829782_state ) ).
% boolean_algebra.disj_one_left
thf(fact_549_sup__top__right,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ top_to5868225466921797218tate_o )
= top_to5868225466921797218tate_o ) ).
% sup_top_right
thf(fact_550_sup__top__right,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ X2 @ top_top_set_state )
= top_top_set_state ) ).
% sup_top_right
thf(fact_551_sup__top__right,axiom,
! [X2: state > $o] :
( ( sup_sup_state_o @ X2 @ top_top_state_o )
= top_top_state_o ) ).
% sup_top_right
thf(fact_552_sup__top__right,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ top_to5262587396890829782_state )
= top_to5262587396890829782_state ) ).
% sup_top_right
thf(fact_553_sup__top__left,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ top_to5868225466921797218tate_o @ X2 )
= top_to5868225466921797218tate_o ) ).
% sup_top_left
thf(fact_554_sup__top__left,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ top_top_set_state @ X2 )
= top_top_set_state ) ).
% sup_top_left
thf(fact_555_sup__top__left,axiom,
! [X2: state > $o] :
( ( sup_sup_state_o @ top_top_state_o @ X2 )
= top_top_state_o ) ).
% sup_top_left
thf(fact_556_sup__top__left,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ top_to5262587396890829782_state @ X2 )
= top_to5262587396890829782_state ) ).
% sup_top_left
thf(fact_557_Un__empty,axiom,
! [A: set_state,B: set_state] :
( ( ( sup_sup_set_state @ A @ B )
= bot_bot_set_state )
= ( ( A = bot_bot_set_state )
& ( B = bot_bot_set_state ) ) ) ).
% Un_empty
thf(fact_558_Un__empty,axiom,
! [A: set_set_state,B: set_set_state] :
( ( ( sup_su4188871578264421970_state @ A @ B )
= bot_bo2271482359692755898_state )
= ( ( A = bot_bo2271482359692755898_state )
& ( B = bot_bo2271482359692755898_state ) ) ) ).
% Un_empty
thf(fact_559_Un__subset__iff,axiom,
! [A: set_set_state,B: set_set_state,C2: set_set_state] :
( ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ A @ B ) @ C2 )
= ( ( ord_le5175021213330142598_state @ A @ C2 )
& ( ord_le5175021213330142598_state @ B @ C2 ) ) ) ).
% Un_subset_iff
thf(fact_560_Un__subset__iff,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A @ B ) @ C2 )
= ( ( ord_le2494988322063910608_state @ A @ C2 )
& ( ord_le2494988322063910608_state @ B @ C2 ) ) ) ).
% Un_subset_iff
thf(fact_561_atLeast__empty__triv,axiom,
( ( set_or922425460254742171_state @ bot_bo2271482359692755898_state )
= top_to3598970937283095436_state ) ).
% atLeast_empty_triv
thf(fact_562_atLeast__empty__triv,axiom,
( ( set_or6477372120337742821_state @ bot_bot_set_state )
= top_to5262587396890829782_state ) ).
% atLeast_empty_triv
thf(fact_563_boolean__algebra_Ocompl__zero,axiom,
( ( uminus3809647891681718284tate_o @ bot_bot_state_o )
= top_top_state_o ) ).
% boolean_algebra.compl_zero
thf(fact_564_boolean__algebra_Ocompl__zero,axiom,
( ( uminus4035512285888117871_state @ bot_bo2271482359692755898_state )
= top_to5262587396890829782_state ) ).
% boolean_algebra.compl_zero
thf(fact_565_boolean__algebra_Ocompl__zero,axiom,
( ( uminus472742206872269241_state @ bot_bot_set_state )
= top_top_set_state ) ).
% boolean_algebra.compl_zero
thf(fact_566_boolean__algebra_Ocompl__one,axiom,
( ( uminus3809647891681718284tate_o @ top_top_state_o )
= bot_bot_state_o ) ).
% boolean_algebra.compl_one
thf(fact_567_boolean__algebra_Ocompl__one,axiom,
( ( uminus4035512285888117871_state @ top_to5262587396890829782_state )
= bot_bo2271482359692755898_state ) ).
% boolean_algebra.compl_one
thf(fact_568_boolean__algebra_Ocompl__one,axiom,
( ( uminus472742206872269241_state @ top_top_set_state )
= bot_bot_set_state ) ).
% boolean_algebra.compl_one
thf(fact_569_atLeastatMost__empty__iff,axiom,
! [A2: $o > set_state,B3: $o > set_state] :
( ( ( set_or7399831441507084590_state @ A2 @ B3 )
= bot_bo782247444858010053_state )
= ( ~ ( ord_le9189382018855386905_state @ A2 @ B3 ) ) ) ).
% atLeastatMost_empty_iff
thf(fact_570_atLeastatMost__empty__iff,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ( set_or7796883608616495921_state @ A2 @ B3 )
= bot_bo7389043141884672880_state )
= ( ~ ( ord_le5175021213330142598_state @ A2 @ B3 ) ) ) ).
% atLeastatMost_empty_iff
thf(fact_571_atLeastatMost__empty__iff,axiom,
! [A2: set_state,B3: set_state] :
( ( ( set_or701696889746204795_state @ A2 @ B3 )
= bot_bo2271482359692755898_state )
= ( ~ ( ord_le2494988322063910608_state @ A2 @ B3 ) ) ) ).
% atLeastatMost_empty_iff
thf(fact_572_atLeastatMost__empty__iff2,axiom,
! [A2: $o > set_state,B3: $o > set_state] :
( ( bot_bo782247444858010053_state
= ( set_or7399831441507084590_state @ A2 @ B3 ) )
= ( ~ ( ord_le9189382018855386905_state @ A2 @ B3 ) ) ) ).
% atLeastatMost_empty_iff2
thf(fact_573_atLeastatMost__empty__iff2,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( bot_bo7389043141884672880_state
= ( set_or7796883608616495921_state @ A2 @ B3 ) )
= ( ~ ( ord_le5175021213330142598_state @ A2 @ B3 ) ) ) ).
% atLeastatMost_empty_iff2
thf(fact_574_atLeastatMost__empty__iff2,axiom,
! [A2: set_state,B3: set_state] :
( ( bot_bo2271482359692755898_state
= ( set_or701696889746204795_state @ A2 @ B3 ) )
= ( ~ ( ord_le2494988322063910608_state @ A2 @ B3 ) ) ) ).
% atLeastatMost_empty_iff2
thf(fact_575_boolean__algebra_Odisj__cancel__right,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ ( uminus7723173452139699081tate_o @ X2 ) )
= top_to5868225466921797218tate_o ) ).
% boolean_algebra.disj_cancel_right
thf(fact_576_boolean__algebra_Odisj__cancel__right,axiom,
! [X2: state > $o] :
( ( sup_sup_state_o @ X2 @ ( uminus3809647891681718284tate_o @ X2 ) )
= top_top_state_o ) ).
% boolean_algebra.disj_cancel_right
thf(fact_577_boolean__algebra_Odisj__cancel__right,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ ( uminus4035512285888117871_state @ X2 ) )
= top_to5262587396890829782_state ) ).
% boolean_algebra.disj_cancel_right
thf(fact_578_boolean__algebra_Odisj__cancel__right,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ X2 @ ( uminus472742206872269241_state @ X2 ) )
= top_top_set_state ) ).
% boolean_algebra.disj_cancel_right
thf(fact_579_boolean__algebra_Odisj__cancel__left,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ ( uminus7723173452139699081tate_o @ X2 ) @ X2 )
= top_to5868225466921797218tate_o ) ).
% boolean_algebra.disj_cancel_left
thf(fact_580_boolean__algebra_Odisj__cancel__left,axiom,
! [X2: state > $o] :
( ( sup_sup_state_o @ ( uminus3809647891681718284tate_o @ X2 ) @ X2 )
= top_top_state_o ) ).
% boolean_algebra.disj_cancel_left
thf(fact_581_boolean__algebra_Odisj__cancel__left,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ ( uminus4035512285888117871_state @ X2 ) @ X2 )
= top_to5262587396890829782_state ) ).
% boolean_algebra.disj_cancel_left
thf(fact_582_boolean__algebra_Odisj__cancel__left,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ ( uminus472742206872269241_state @ X2 ) @ X2 )
= top_top_set_state ) ).
% boolean_algebra.disj_cancel_left
thf(fact_583_sup__compl__top__left2,axiom,
! [X2: state > state > $o,Y: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ ( uminus7723173452139699081tate_o @ X2 ) @ Y ) )
= top_to5868225466921797218tate_o ) ).
% sup_compl_top_left2
thf(fact_584_sup__compl__top__left2,axiom,
! [X2: state > $o,Y: state > $o] :
( ( sup_sup_state_o @ X2 @ ( sup_sup_state_o @ ( uminus3809647891681718284tate_o @ X2 ) @ Y ) )
= top_top_state_o ) ).
% sup_compl_top_left2
thf(fact_585_sup__compl__top__left2,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ ( sup_su4188871578264421970_state @ ( uminus4035512285888117871_state @ X2 ) @ Y ) )
= top_to5262587396890829782_state ) ).
% sup_compl_top_left2
thf(fact_586_sup__compl__top__left2,axiom,
! [X2: set_state,Y: set_state] :
( ( sup_sup_set_state @ X2 @ ( sup_sup_set_state @ ( uminus472742206872269241_state @ X2 ) @ Y ) )
= top_top_set_state ) ).
% sup_compl_top_left2
thf(fact_587_sup__compl__top__left1,axiom,
! [X2: state > state > $o,Y: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ ( uminus7723173452139699081tate_o @ X2 ) @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) )
= top_to5868225466921797218tate_o ) ).
% sup_compl_top_left1
thf(fact_588_sup__compl__top__left1,axiom,
! [X2: state > $o,Y: state > $o] :
( ( sup_sup_state_o @ ( uminus3809647891681718284tate_o @ X2 ) @ ( sup_sup_state_o @ X2 @ Y ) )
= top_top_state_o ) ).
% sup_compl_top_left1
thf(fact_589_sup__compl__top__left1,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( sup_su4188871578264421970_state @ ( uminus4035512285888117871_state @ X2 ) @ ( sup_su4188871578264421970_state @ X2 @ Y ) )
= top_to5262587396890829782_state ) ).
% sup_compl_top_left1
thf(fact_590_sup__compl__top__left1,axiom,
! [X2: set_state,Y: set_state] :
( ( sup_sup_set_state @ ( uminus472742206872269241_state @ X2 ) @ ( sup_sup_set_state @ X2 @ Y ) )
= top_top_set_state ) ).
% sup_compl_top_left1
thf(fact_591_atLeastatMost__empty,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( ord_le8280034978549525370_state @ B3 @ A2 )
=> ( ( set_or7796883608616495921_state @ A2 @ B3 )
= bot_bo7389043141884672880_state ) ) ).
% atLeastatMost_empty
thf(fact_592_atLeastatMost__empty,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_less_set_state @ B3 @ A2 )
=> ( ( set_or701696889746204795_state @ A2 @ B3 )
= bot_bo2271482359692755898_state ) ) ).
% atLeastatMost_empty
thf(fact_593_atLeastLessThan__empty,axiom,
! [B3: $o > set_state,A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ B3 @ A2 )
=> ( ( set_or8134177505681183498_state @ A2 @ B3 )
= bot_bo782247444858010053_state ) ) ).
% atLeastLessThan_empty
thf(fact_594_atLeastLessThan__empty,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( ord_le5175021213330142598_state @ B3 @ A2 )
=> ( ( set_or5996981303281673813_state @ A2 @ B3 )
= bot_bo7389043141884672880_state ) ) ).
% atLeastLessThan_empty
thf(fact_595_atLeastLessThan__empty,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ( ( set_or2838015025653527455_state @ A2 @ B3 )
= bot_bo2271482359692755898_state ) ) ).
% atLeastLessThan_empty
thf(fact_596_atLeastLessThan__empty__iff,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ( set_or5996981303281673813_state @ A2 @ B3 )
= bot_bo7389043141884672880_state )
= ( ~ ( ord_le8280034978549525370_state @ A2 @ B3 ) ) ) ).
% atLeastLessThan_empty_iff
thf(fact_597_atLeastLessThan__empty__iff,axiom,
! [A2: set_state,B3: set_state] :
( ( ( set_or2838015025653527455_state @ A2 @ B3 )
= bot_bo2271482359692755898_state )
= ( ~ ( ord_less_set_state @ A2 @ B3 ) ) ) ).
% atLeastLessThan_empty_iff
thf(fact_598_atLeastLessThan__empty__iff2,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( bot_bo7389043141884672880_state
= ( set_or5996981303281673813_state @ A2 @ B3 ) )
= ( ~ ( ord_le8280034978549525370_state @ A2 @ B3 ) ) ) ).
% atLeastLessThan_empty_iff2
thf(fact_599_atLeastLessThan__empty__iff2,axiom,
! [A2: set_state,B3: set_state] :
( ( bot_bo2271482359692755898_state
= ( set_or2838015025653527455_state @ A2 @ B3 ) )
= ( ~ ( ord_less_set_state @ A2 @ B3 ) ) ) ).
% atLeastLessThan_empty_iff2
thf(fact_600_greaterThanAtMost__iff,axiom,
! [I: $o > set_state,L: $o > set_state,U: $o > set_state] :
( ( member_o_set_state @ I @ ( set_or9083347566284363977_state @ L @ U ) )
= ( ( ord_less_o_set_state @ L @ I )
& ( ord_le9189382018855386905_state @ I @ U ) ) ) ).
% greaterThanAtMost_iff
thf(fact_601_greaterThanAtMost__iff,axiom,
! [I: set_set_state,L: set_set_state,U: set_set_state] :
( ( member_set_set_state @ I @ ( set_or8261726110466482134_state @ L @ U ) )
= ( ( ord_le8280034978549525370_state @ L @ I )
& ( ord_le5175021213330142598_state @ I @ U ) ) ) ).
% greaterThanAtMost_iff
thf(fact_602_greaterThanAtMost__iff,axiom,
! [I: set_state,L: set_state,U: set_state] :
( ( member_set_state @ I @ ( set_or5184245929044373792_state @ L @ U ) )
= ( ( ord_less_set_state @ L @ I )
& ( ord_le2494988322063910608_state @ I @ U ) ) ) ).
% greaterThanAtMost_iff
thf(fact_603_greaterThanAtMost__empty,axiom,
! [L: $o > set_state,K: $o > set_state] :
( ( ord_le9189382018855386905_state @ L @ K )
=> ( ( set_or9083347566284363977_state @ K @ L )
= bot_bo782247444858010053_state ) ) ).
% greaterThanAtMost_empty
thf(fact_604_greaterThanAtMost__empty,axiom,
! [L: set_set_state,K: set_set_state] :
( ( ord_le5175021213330142598_state @ L @ K )
=> ( ( set_or8261726110466482134_state @ K @ L )
= bot_bo7389043141884672880_state ) ) ).
% greaterThanAtMost_empty
thf(fact_605_greaterThanAtMost__empty,axiom,
! [L: set_state,K: set_state] :
( ( ord_le2494988322063910608_state @ L @ K )
=> ( ( set_or5184245929044373792_state @ K @ L )
= bot_bo2271482359692755898_state ) ) ).
% greaterThanAtMost_empty
thf(fact_606_greaterThanAtMost__empty__iff2,axiom,
! [K: set_set_state,L: set_set_state] :
( ( bot_bo7389043141884672880_state
= ( set_or8261726110466482134_state @ K @ L ) )
= ( ~ ( ord_le8280034978549525370_state @ K @ L ) ) ) ).
% greaterThanAtMost_empty_iff2
thf(fact_607_greaterThanAtMost__empty__iff2,axiom,
! [K: set_state,L: set_state] :
( ( bot_bo2271482359692755898_state
= ( set_or5184245929044373792_state @ K @ L ) )
= ( ~ ( ord_less_set_state @ K @ L ) ) ) ).
% greaterThanAtMost_empty_iff2
thf(fact_608_greaterThanAtMost__empty__iff,axiom,
! [K: set_set_state,L: set_set_state] :
( ( ( set_or8261726110466482134_state @ K @ L )
= bot_bo7389043141884672880_state )
= ( ~ ( ord_le8280034978549525370_state @ K @ L ) ) ) ).
% greaterThanAtMost_empty_iff
thf(fact_609_greaterThanAtMost__empty__iff,axiom,
! [K: set_state,L: set_state] :
( ( ( set_or5184245929044373792_state @ K @ L )
= bot_bo2271482359692755898_state )
= ( ~ ( ord_less_set_state @ K @ L ) ) ) ).
% greaterThanAtMost_empty_iff
thf(fact_610_greaterThanLessThan__empty,axiom,
! [L: $o > set_state,K: $o > set_state] :
( ( ord_le9189382018855386905_state @ L @ K )
=> ( ( set_or9151442426322445605_state @ K @ L )
= bot_bo782247444858010053_state ) ) ).
% greaterThanLessThan_empty
thf(fact_611_greaterThanLessThan__empty,axiom,
! [L: set_set_state,K: set_set_state] :
( ( ord_le5175021213330142598_state @ L @ K )
=> ( ( set_or4346910941253671034_state @ K @ L )
= bot_bo7389043141884672880_state ) ) ).
% greaterThanLessThan_empty
thf(fact_612_greaterThanLessThan__empty,axiom,
! [L: set_state,K: set_state] :
( ( ord_le2494988322063910608_state @ L @ K )
=> ( ( set_or421293776985356740_state @ K @ L )
= bot_bo2271482359692755898_state ) ) ).
% greaterThanLessThan_empty
thf(fact_613_UnE,axiom,
! [C: set_set_state,A: set_set_set_state,B: set_set_set_state] :
( ( member_set_set_state @ C @ ( sup_su3277220503338409480_state @ A @ B ) )
=> ( ~ ( member_set_set_state @ C @ A )
=> ( member_set_set_state @ C @ B ) ) ) ).
% UnE
thf(fact_614_UnE,axiom,
! [C: set_state,A: set_set_state,B: set_set_state] :
( ( member_set_state @ C @ ( sup_su4188871578264421970_state @ A @ B ) )
=> ( ~ ( member_set_state @ C @ A )
=> ( member_set_state @ C @ B ) ) ) ).
% UnE
thf(fact_615_UnE,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( sup_sup_set_state @ A @ B ) )
=> ( ~ ( member_state @ C @ A )
=> ( member_state @ C @ B ) ) ) ).
% UnE
thf(fact_616_UnI1,axiom,
! [C: set_set_state,A: set_set_set_state,B: set_set_set_state] :
( ( member_set_set_state @ C @ A )
=> ( member_set_set_state @ C @ ( sup_su3277220503338409480_state @ A @ B ) ) ) ).
% UnI1
thf(fact_617_UnI1,axiom,
! [C: set_state,A: set_set_state,B: set_set_state] :
( ( member_set_state @ C @ A )
=> ( member_set_state @ C @ ( sup_su4188871578264421970_state @ A @ B ) ) ) ).
% UnI1
thf(fact_618_UnI1,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ A )
=> ( member_state @ C @ ( sup_sup_set_state @ A @ B ) ) ) ).
% UnI1
thf(fact_619_UnI2,axiom,
! [C: set_set_state,B: set_set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ C @ B )
=> ( member_set_set_state @ C @ ( sup_su3277220503338409480_state @ A @ B ) ) ) ).
% UnI2
thf(fact_620_UnI2,axiom,
! [C: set_state,B: set_set_state,A: set_set_state] :
( ( member_set_state @ C @ B )
=> ( member_set_state @ C @ ( sup_su4188871578264421970_state @ A @ B ) ) ) ).
% UnI2
thf(fact_621_UnI2,axiom,
! [C: state,B: set_state,A: set_state] :
( ( member_state @ C @ B )
=> ( member_state @ C @ ( sup_sup_set_state @ A @ B ) ) ) ).
% UnI2
thf(fact_622_bex__Un,axiom,
! [A: set_state,B: set_state,P: state > $o] :
( ( ? [X3: state] :
( ( member_state @ X3 @ ( sup_sup_set_state @ A @ B ) )
& ( P @ X3 ) ) )
= ( ? [X3: state] :
( ( member_state @ X3 @ A )
& ( P @ X3 ) )
| ? [X3: state] :
( ( member_state @ X3 @ B )
& ( P @ X3 ) ) ) ) ).
% bex_Un
thf(fact_623_bex__Un,axiom,
! [A: set_set_state,B: set_set_state,P: set_state > $o] :
( ( ? [X3: set_state] :
( ( member_set_state @ X3 @ ( sup_su4188871578264421970_state @ A @ B ) )
& ( P @ X3 ) ) )
= ( ? [X3: set_state] :
( ( member_set_state @ X3 @ A )
& ( P @ X3 ) )
| ? [X3: set_state] :
( ( member_set_state @ X3 @ B )
& ( P @ X3 ) ) ) ) ).
% bex_Un
thf(fact_624_emptyE,axiom,
! [A2: set_set_state] :
~ ( member_set_set_state @ A2 @ bot_bo7389043141884672880_state ) ).
% emptyE
thf(fact_625_emptyE,axiom,
! [A2: set_state] :
~ ( member_set_state @ A2 @ bot_bo2271482359692755898_state ) ).
% emptyE
thf(fact_626_emptyE,axiom,
! [A2: state] :
~ ( member_state @ A2 @ bot_bot_set_state ) ).
% emptyE
thf(fact_627_ball__Un,axiom,
! [A: set_state,B: set_state,P: state > $o] :
( ( ! [X3: state] :
( ( member_state @ X3 @ ( sup_sup_set_state @ A @ B ) )
=> ( P @ X3 ) ) )
= ( ! [X3: state] :
( ( member_state @ X3 @ A )
=> ( P @ X3 ) )
& ! [X3: state] :
( ( member_state @ X3 @ B )
=> ( P @ X3 ) ) ) ) ).
% ball_Un
thf(fact_628_ball__Un,axiom,
! [A: set_set_state,B: set_set_state,P: set_state > $o] :
( ( ! [X3: set_state] :
( ( member_set_state @ X3 @ ( sup_su4188871578264421970_state @ A @ B ) )
=> ( P @ X3 ) ) )
= ( ! [X3: set_state] :
( ( member_set_state @ X3 @ A )
=> ( P @ X3 ) )
& ! [X3: set_state] :
( ( member_set_state @ X3 @ B )
=> ( P @ X3 ) ) ) ) ).
% ball_Un
thf(fact_629_Un__assoc,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( sup_sup_set_state @ ( sup_sup_set_state @ A @ B ) @ C2 )
= ( sup_sup_set_state @ A @ ( sup_sup_set_state @ B @ C2 ) ) ) ).
% Un_assoc
thf(fact_630_Un__assoc,axiom,
! [A: set_set_state,B: set_set_state,C2: set_set_state] :
( ( sup_su4188871578264421970_state @ ( sup_su4188871578264421970_state @ A @ B ) @ C2 )
= ( sup_su4188871578264421970_state @ A @ ( sup_su4188871578264421970_state @ B @ C2 ) ) ) ).
% Un_assoc
thf(fact_631_equals0D,axiom,
! [A: set_set_set_state,A2: set_set_state] :
( ( A = bot_bo7389043141884672880_state )
=> ~ ( member_set_set_state @ A2 @ A ) ) ).
% equals0D
thf(fact_632_equals0D,axiom,
! [A: set_set_state,A2: set_state] :
( ( A = bot_bo2271482359692755898_state )
=> ~ ( member_set_state @ A2 @ A ) ) ).
% equals0D
thf(fact_633_equals0D,axiom,
! [A: set_state,A2: state] :
( ( A = bot_bot_set_state )
=> ~ ( member_state @ A2 @ A ) ) ).
% equals0D
thf(fact_634_equals0I,axiom,
! [A: set_set_set_state] :
( ! [Y2: set_set_state] :
~ ( member_set_set_state @ Y2 @ A )
=> ( A = bot_bo7389043141884672880_state ) ) ).
% equals0I
thf(fact_635_equals0I,axiom,
! [A: set_set_state] :
( ! [Y2: set_state] :
~ ( member_set_state @ Y2 @ A )
=> ( A = bot_bo2271482359692755898_state ) ) ).
% equals0I
thf(fact_636_equals0I,axiom,
! [A: set_state] :
( ! [Y2: state] :
~ ( member_state @ Y2 @ A )
=> ( A = bot_bot_set_state ) ) ).
% equals0I
thf(fact_637_Un__absorb,axiom,
! [A: set_state] :
( ( sup_sup_set_state @ A @ A )
= A ) ).
% Un_absorb
thf(fact_638_Un__absorb,axiom,
! [A: set_set_state] :
( ( sup_su4188871578264421970_state @ A @ A )
= A ) ).
% Un_absorb
thf(fact_639_Un__commute,axiom,
( sup_sup_set_state
= ( ^ [A3: set_state,B2: set_state] : ( sup_sup_set_state @ B2 @ A3 ) ) ) ).
% Un_commute
thf(fact_640_Un__commute,axiom,
( sup_su4188871578264421970_state
= ( ^ [A3: set_set_state,B2: set_set_state] : ( sup_su4188871578264421970_state @ B2 @ A3 ) ) ) ).
% Un_commute
thf(fact_641_ex__in__conv,axiom,
! [A: set_set_set_state] :
( ( ? [X3: set_set_state] : ( member_set_set_state @ X3 @ A ) )
= ( A != bot_bo7389043141884672880_state ) ) ).
% ex_in_conv
thf(fact_642_ex__in__conv,axiom,
! [A: set_set_state] :
( ( ? [X3: set_state] : ( member_set_state @ X3 @ A ) )
= ( A != bot_bo2271482359692755898_state ) ) ).
% ex_in_conv
thf(fact_643_ex__in__conv,axiom,
! [A: set_state] :
( ( ? [X3: state] : ( member_state @ X3 @ A ) )
= ( A != bot_bot_set_state ) ) ).
% ex_in_conv
thf(fact_644_Un__empty__left,axiom,
! [B: set_state] :
( ( sup_sup_set_state @ bot_bot_set_state @ B )
= B ) ).
% Un_empty_left
thf(fact_645_Un__empty__left,axiom,
! [B: set_set_state] :
( ( sup_su4188871578264421970_state @ bot_bo2271482359692755898_state @ B )
= B ) ).
% Un_empty_left
thf(fact_646_Un__empty__right,axiom,
! [A: set_state] :
( ( sup_sup_set_state @ A @ bot_bot_set_state )
= A ) ).
% Un_empty_right
thf(fact_647_Un__empty__right,axiom,
! [A: set_set_state] :
( ( sup_su4188871578264421970_state @ A @ bot_bo2271482359692755898_state )
= A ) ).
% Un_empty_right
thf(fact_648_Un__left__absorb,axiom,
! [A: set_state,B: set_state] :
( ( sup_sup_set_state @ A @ ( sup_sup_set_state @ A @ B ) )
= ( sup_sup_set_state @ A @ B ) ) ).
% Un_left_absorb
thf(fact_649_Un__left__absorb,axiom,
! [A: set_set_state,B: set_set_state] :
( ( sup_su4188871578264421970_state @ A @ ( sup_su4188871578264421970_state @ A @ B ) )
= ( sup_su4188871578264421970_state @ A @ B ) ) ).
% Un_left_absorb
thf(fact_650_Un__left__commute,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( sup_sup_set_state @ A @ ( sup_sup_set_state @ B @ C2 ) )
= ( sup_sup_set_state @ B @ ( sup_sup_set_state @ A @ C2 ) ) ) ).
% Un_left_commute
thf(fact_651_Un__left__commute,axiom,
! [A: set_set_state,B: set_set_state,C2: set_set_state] :
( ( sup_su4188871578264421970_state @ A @ ( sup_su4188871578264421970_state @ B @ C2 ) )
= ( sup_su4188871578264421970_state @ B @ ( sup_su4188871578264421970_state @ A @ C2 ) ) ) ).
% Un_left_commute
thf(fact_652_inf__sup__aci_I8_J,axiom,
! [X2: set_state,Y: set_state] :
( ( sup_sup_set_state @ X2 @ ( sup_sup_set_state @ X2 @ Y ) )
= ( sup_sup_set_state @ X2 @ Y ) ) ).
% inf_sup_aci(8)
thf(fact_653_inf__sup__aci_I8_J,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ ( sup_su4188871578264421970_state @ X2 @ Y ) )
= ( sup_su4188871578264421970_state @ X2 @ Y ) ) ).
% inf_sup_aci(8)
thf(fact_654_inf__sup__aci_I8_J,axiom,
! [X2: state > state > $o,Y: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) )
= ( sup_su7525921995284788454tate_o @ X2 @ Y ) ) ).
% inf_sup_aci(8)
thf(fact_655_inf__sup__aci_I7_J,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( sup_sup_set_state @ X2 @ ( sup_sup_set_state @ Y @ Z2 ) )
= ( sup_sup_set_state @ Y @ ( sup_sup_set_state @ X2 @ Z2 ) ) ) ).
% inf_sup_aci(7)
thf(fact_656_inf__sup__aci_I7_J,axiom,
! [X2: set_set_state,Y: set_set_state,Z2: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ ( sup_su4188871578264421970_state @ Y @ Z2 ) )
= ( sup_su4188871578264421970_state @ Y @ ( sup_su4188871578264421970_state @ X2 @ Z2 ) ) ) ).
% inf_sup_aci(7)
thf(fact_657_inf__sup__aci_I7_J,axiom,
! [X2: state > state > $o,Y: state > state > $o,Z2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ Y @ Z2 ) )
= ( sup_su7525921995284788454tate_o @ Y @ ( sup_su7525921995284788454tate_o @ X2 @ Z2 ) ) ) ).
% inf_sup_aci(7)
thf(fact_658_inf__sup__aci_I6_J,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( sup_sup_set_state @ ( sup_sup_set_state @ X2 @ Y ) @ Z2 )
= ( sup_sup_set_state @ X2 @ ( sup_sup_set_state @ Y @ Z2 ) ) ) ).
% inf_sup_aci(6)
thf(fact_659_inf__sup__aci_I6_J,axiom,
! [X2: set_set_state,Y: set_set_state,Z2: set_set_state] :
( ( sup_su4188871578264421970_state @ ( sup_su4188871578264421970_state @ X2 @ Y ) @ Z2 )
= ( sup_su4188871578264421970_state @ X2 @ ( sup_su4188871578264421970_state @ Y @ Z2 ) ) ) ).
% inf_sup_aci(6)
thf(fact_660_inf__sup__aci_I6_J,axiom,
! [X2: state > state > $o,Y: state > state > $o,Z2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) @ Z2 )
= ( sup_su7525921995284788454tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ Y @ Z2 ) ) ) ).
% inf_sup_aci(6)
thf(fact_661_inf__sup__aci_I5_J,axiom,
( sup_sup_set_state
= ( ^ [X3: set_state,Y4: set_state] : ( sup_sup_set_state @ Y4 @ X3 ) ) ) ).
% inf_sup_aci(5)
thf(fact_662_inf__sup__aci_I5_J,axiom,
( sup_su4188871578264421970_state
= ( ^ [X3: set_set_state,Y4: set_set_state] : ( sup_su4188871578264421970_state @ Y4 @ X3 ) ) ) ).
% inf_sup_aci(5)
thf(fact_663_inf__sup__aci_I5_J,axiom,
( sup_su7525921995284788454tate_o
= ( ^ [X3: state > state > $o,Y4: state > state > $o] : ( sup_su7525921995284788454tate_o @ Y4 @ X3 ) ) ) ).
% inf_sup_aci(5)
thf(fact_664_sup_Oassoc,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( sup_sup_set_state @ ( sup_sup_set_state @ A2 @ B3 ) @ C )
= ( sup_sup_set_state @ A2 @ ( sup_sup_set_state @ B3 @ C ) ) ) ).
% sup.assoc
thf(fact_665_sup_Oassoc,axiom,
! [A2: set_set_state,B3: set_set_state,C: set_set_state] :
( ( sup_su4188871578264421970_state @ ( sup_su4188871578264421970_state @ A2 @ B3 ) @ C )
= ( sup_su4188871578264421970_state @ A2 @ ( sup_su4188871578264421970_state @ B3 @ C ) ) ) ).
% sup.assoc
thf(fact_666_sup_Oassoc,axiom,
! [A2: state > state > $o,B3: state > state > $o,C: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) @ C )
= ( sup_su7525921995284788454tate_o @ A2 @ ( sup_su7525921995284788454tate_o @ B3 @ C ) ) ) ).
% sup.assoc
thf(fact_667_sup__assoc,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( sup_sup_set_state @ ( sup_sup_set_state @ X2 @ Y ) @ Z2 )
= ( sup_sup_set_state @ X2 @ ( sup_sup_set_state @ Y @ Z2 ) ) ) ).
% sup_assoc
thf(fact_668_sup__assoc,axiom,
! [X2: set_set_state,Y: set_set_state,Z2: set_set_state] :
( ( sup_su4188871578264421970_state @ ( sup_su4188871578264421970_state @ X2 @ Y ) @ Z2 )
= ( sup_su4188871578264421970_state @ X2 @ ( sup_su4188871578264421970_state @ Y @ Z2 ) ) ) ).
% sup_assoc
thf(fact_669_sup__assoc,axiom,
! [X2: state > state > $o,Y: state > state > $o,Z2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) @ Z2 )
= ( sup_su7525921995284788454tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ Y @ Z2 ) ) ) ).
% sup_assoc
thf(fact_670_sup_Ocommute,axiom,
( sup_sup_set_state
= ( ^ [A4: set_state,B4: set_state] : ( sup_sup_set_state @ B4 @ A4 ) ) ) ).
% sup.commute
thf(fact_671_sup_Ocommute,axiom,
( sup_su4188871578264421970_state
= ( ^ [A4: set_set_state,B4: set_set_state] : ( sup_su4188871578264421970_state @ B4 @ A4 ) ) ) ).
% sup.commute
thf(fact_672_sup_Ocommute,axiom,
( sup_su7525921995284788454tate_o
= ( ^ [A4: state > state > $o,B4: state > state > $o] : ( sup_su7525921995284788454tate_o @ B4 @ A4 ) ) ) ).
% sup.commute
thf(fact_673_sup__commute,axiom,
( sup_sup_set_state
= ( ^ [X3: set_state,Y4: set_state] : ( sup_sup_set_state @ Y4 @ X3 ) ) ) ).
% sup_commute
thf(fact_674_sup__commute,axiom,
( sup_su4188871578264421970_state
= ( ^ [X3: set_set_state,Y4: set_set_state] : ( sup_su4188871578264421970_state @ Y4 @ X3 ) ) ) ).
% sup_commute
thf(fact_675_sup__commute,axiom,
( sup_su7525921995284788454tate_o
= ( ^ [X3: state > state > $o,Y4: state > state > $o] : ( sup_su7525921995284788454tate_o @ Y4 @ X3 ) ) ) ).
% sup_commute
thf(fact_676_boolean__algebra__cancel_Osup1,axiom,
! [A: set_state,K: set_state,A2: set_state,B3: set_state] :
( ( A
= ( sup_sup_set_state @ K @ A2 ) )
=> ( ( sup_sup_set_state @ A @ B3 )
= ( sup_sup_set_state @ K @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.sup1
thf(fact_677_boolean__algebra__cancel_Osup1,axiom,
! [A: set_set_state,K: set_set_state,A2: set_set_state,B3: set_set_state] :
( ( A
= ( sup_su4188871578264421970_state @ K @ A2 ) )
=> ( ( sup_su4188871578264421970_state @ A @ B3 )
= ( sup_su4188871578264421970_state @ K @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.sup1
thf(fact_678_boolean__algebra__cancel_Osup1,axiom,
! [A: state > state > $o,K: state > state > $o,A2: state > state > $o,B3: state > state > $o] :
( ( A
= ( sup_su7525921995284788454tate_o @ K @ A2 ) )
=> ( ( sup_su7525921995284788454tate_o @ A @ B3 )
= ( sup_su7525921995284788454tate_o @ K @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.sup1
thf(fact_679_boolean__algebra__cancel_Osup2,axiom,
! [B: set_state,K: set_state,B3: set_state,A2: set_state] :
( ( B
= ( sup_sup_set_state @ K @ B3 ) )
=> ( ( sup_sup_set_state @ A2 @ B )
= ( sup_sup_set_state @ K @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.sup2
thf(fact_680_boolean__algebra__cancel_Osup2,axiom,
! [B: set_set_state,K: set_set_state,B3: set_set_state,A2: set_set_state] :
( ( B
= ( sup_su4188871578264421970_state @ K @ B3 ) )
=> ( ( sup_su4188871578264421970_state @ A2 @ B )
= ( sup_su4188871578264421970_state @ K @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.sup2
thf(fact_681_boolean__algebra__cancel_Osup2,axiom,
! [B: state > state > $o,K: state > state > $o,B3: state > state > $o,A2: state > state > $o] :
( ( B
= ( sup_su7525921995284788454tate_o @ K @ B3 ) )
=> ( ( sup_su7525921995284788454tate_o @ A2 @ B )
= ( sup_su7525921995284788454tate_o @ K @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.sup2
thf(fact_682_sup_Oleft__commute,axiom,
! [B3: set_state,A2: set_state,C: set_state] :
( ( sup_sup_set_state @ B3 @ ( sup_sup_set_state @ A2 @ C ) )
= ( sup_sup_set_state @ A2 @ ( sup_sup_set_state @ B3 @ C ) ) ) ).
% sup.left_commute
thf(fact_683_sup_Oleft__commute,axiom,
! [B3: set_set_state,A2: set_set_state,C: set_set_state] :
( ( sup_su4188871578264421970_state @ B3 @ ( sup_su4188871578264421970_state @ A2 @ C ) )
= ( sup_su4188871578264421970_state @ A2 @ ( sup_su4188871578264421970_state @ B3 @ C ) ) ) ).
% sup.left_commute
thf(fact_684_sup_Oleft__commute,axiom,
! [B3: state > state > $o,A2: state > state > $o,C: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ B3 @ ( sup_su7525921995284788454tate_o @ A2 @ C ) )
= ( sup_su7525921995284788454tate_o @ A2 @ ( sup_su7525921995284788454tate_o @ B3 @ C ) ) ) ).
% sup.left_commute
thf(fact_685_sup__left__commute,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( sup_sup_set_state @ X2 @ ( sup_sup_set_state @ Y @ Z2 ) )
= ( sup_sup_set_state @ Y @ ( sup_sup_set_state @ X2 @ Z2 ) ) ) ).
% sup_left_commute
thf(fact_686_sup__left__commute,axiom,
! [X2: set_set_state,Y: set_set_state,Z2: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ ( sup_su4188871578264421970_state @ Y @ Z2 ) )
= ( sup_su4188871578264421970_state @ Y @ ( sup_su4188871578264421970_state @ X2 @ Z2 ) ) ) ).
% sup_left_commute
thf(fact_687_sup__left__commute,axiom,
! [X2: state > state > $o,Y: state > state > $o,Z2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ Y @ Z2 ) )
= ( sup_su7525921995284788454tate_o @ Y @ ( sup_su7525921995284788454tate_o @ X2 @ Z2 ) ) ) ).
% sup_left_commute
thf(fact_688_boolean__algebra_Odisj__zero__right,axiom,
! [X2: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X2 @ bot_bo3298213311409307006tate_o )
= X2 ) ).
% boolean_algebra.disj_zero_right
thf(fact_689_boolean__algebra_Odisj__zero__right,axiom,
! [X2: set_state] :
( ( sup_sup_set_state @ X2 @ bot_bot_set_state )
= X2 ) ).
% boolean_algebra.disj_zero_right
thf(fact_690_boolean__algebra_Odisj__zero__right,axiom,
! [X2: set_set_state] :
( ( sup_su4188871578264421970_state @ X2 @ bot_bo2271482359692755898_state )
= X2 ) ).
% boolean_algebra.disj_zero_right
thf(fact_691_sup__fun__def,axiom,
( sup_su7525921995284788454tate_o
= ( ^ [F2: state > state > $o,G: state > state > $o,X3: state] : ( sup_sup_state_o @ ( F2 @ X3 ) @ ( G @ X3 ) ) ) ) ).
% sup_fun_def
thf(fact_692_inf__sup__ord_I4_J,axiom,
! [Y: state > state > $o,X2: state > state > $o] : ( ord_le4344933087531911346tate_o @ Y @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) ) ).
% inf_sup_ord(4)
thf(fact_693_inf__sup__ord_I4_J,axiom,
! [Y: $o > set_state,X2: $o > set_state] : ( ord_le9189382018855386905_state @ Y @ ( sup_sup_o_set_state @ X2 @ Y ) ) ).
% inf_sup_ord(4)
thf(fact_694_inf__sup__ord_I4_J,axiom,
! [Y: set_set_state,X2: set_set_state] : ( ord_le5175021213330142598_state @ Y @ ( sup_su4188871578264421970_state @ X2 @ Y ) ) ).
% inf_sup_ord(4)
thf(fact_695_inf__sup__ord_I4_J,axiom,
! [Y: set_state,X2: set_state] : ( ord_le2494988322063910608_state @ Y @ ( sup_sup_set_state @ X2 @ Y ) ) ).
% inf_sup_ord(4)
thf(fact_696_inf__sup__ord_I3_J,axiom,
! [X2: state > state > $o,Y: state > state > $o] : ( ord_le4344933087531911346tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) ) ).
% inf_sup_ord(3)
thf(fact_697_inf__sup__ord_I3_J,axiom,
! [X2: $o > set_state,Y: $o > set_state] : ( ord_le9189382018855386905_state @ X2 @ ( sup_sup_o_set_state @ X2 @ Y ) ) ).
% inf_sup_ord(3)
thf(fact_698_inf__sup__ord_I3_J,axiom,
! [X2: set_set_state,Y: set_set_state] : ( ord_le5175021213330142598_state @ X2 @ ( sup_su4188871578264421970_state @ X2 @ Y ) ) ).
% inf_sup_ord(3)
thf(fact_699_inf__sup__ord_I3_J,axiom,
! [X2: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ X2 @ ( sup_sup_set_state @ X2 @ Y ) ) ).
% inf_sup_ord(3)
thf(fact_700_le__supE,axiom,
! [A2: state > state > $o,B3: state > state > $o,X2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) @ X2 )
=> ~ ( ( ord_le4344933087531911346tate_o @ A2 @ X2 )
=> ~ ( ord_le4344933087531911346tate_o @ B3 @ X2 ) ) ) ).
% le_supE
thf(fact_701_le__supE,axiom,
! [A2: $o > set_state,B3: $o > set_state,X2: $o > set_state] :
( ( ord_le9189382018855386905_state @ ( sup_sup_o_set_state @ A2 @ B3 ) @ X2 )
=> ~ ( ( ord_le9189382018855386905_state @ A2 @ X2 )
=> ~ ( ord_le9189382018855386905_state @ B3 @ X2 ) ) ) ).
% le_supE
thf(fact_702_le__supE,axiom,
! [A2: set_set_state,B3: set_set_state,X2: set_set_state] :
( ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ A2 @ B3 ) @ X2 )
=> ~ ( ( ord_le5175021213330142598_state @ A2 @ X2 )
=> ~ ( ord_le5175021213330142598_state @ B3 @ X2 ) ) ) ).
% le_supE
thf(fact_703_le__supE,axiom,
! [A2: set_state,B3: set_state,X2: set_state] :
( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A2 @ B3 ) @ X2 )
=> ~ ( ( ord_le2494988322063910608_state @ A2 @ X2 )
=> ~ ( ord_le2494988322063910608_state @ B3 @ X2 ) ) ) ).
% le_supE
thf(fact_704_le__supI,axiom,
! [A2: state > state > $o,X2: state > state > $o,B3: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ A2 @ X2 )
=> ( ( ord_le4344933087531911346tate_o @ B3 @ X2 )
=> ( ord_le4344933087531911346tate_o @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) @ X2 ) ) ) ).
% le_supI
thf(fact_705_le__supI,axiom,
! [A2: $o > set_state,X2: $o > set_state,B3: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ X2 )
=> ( ( ord_le9189382018855386905_state @ B3 @ X2 )
=> ( ord_le9189382018855386905_state @ ( sup_sup_o_set_state @ A2 @ B3 ) @ X2 ) ) ) ).
% le_supI
thf(fact_706_le__supI,axiom,
! [A2: set_set_state,X2: set_set_state,B3: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ X2 )
=> ( ( ord_le5175021213330142598_state @ B3 @ X2 )
=> ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ A2 @ B3 ) @ X2 ) ) ) ).
% le_supI
thf(fact_707_le__supI,axiom,
! [A2: set_state,X2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ X2 )
=> ( ( ord_le2494988322063910608_state @ B3 @ X2 )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A2 @ B3 ) @ X2 ) ) ) ).
% le_supI
thf(fact_708_sup__ge1,axiom,
! [X2: state > state > $o,Y: state > state > $o] : ( ord_le4344933087531911346tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) ) ).
% sup_ge1
thf(fact_709_sup__ge1,axiom,
! [X2: $o > set_state,Y: $o > set_state] : ( ord_le9189382018855386905_state @ X2 @ ( sup_sup_o_set_state @ X2 @ Y ) ) ).
% sup_ge1
thf(fact_710_sup__ge1,axiom,
! [X2: set_set_state,Y: set_set_state] : ( ord_le5175021213330142598_state @ X2 @ ( sup_su4188871578264421970_state @ X2 @ Y ) ) ).
% sup_ge1
thf(fact_711_sup__ge1,axiom,
! [X2: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ X2 @ ( sup_sup_set_state @ X2 @ Y ) ) ).
% sup_ge1
thf(fact_712_sup__ge2,axiom,
! [Y: state > state > $o,X2: state > state > $o] : ( ord_le4344933087531911346tate_o @ Y @ ( sup_su7525921995284788454tate_o @ X2 @ Y ) ) ).
% sup_ge2
thf(fact_713_sup__ge2,axiom,
! [Y: $o > set_state,X2: $o > set_state] : ( ord_le9189382018855386905_state @ Y @ ( sup_sup_o_set_state @ X2 @ Y ) ) ).
% sup_ge2
thf(fact_714_sup__ge2,axiom,
! [Y: set_set_state,X2: set_set_state] : ( ord_le5175021213330142598_state @ Y @ ( sup_su4188871578264421970_state @ X2 @ Y ) ) ).
% sup_ge2
thf(fact_715_sup__ge2,axiom,
! [Y: set_state,X2: set_state] : ( ord_le2494988322063910608_state @ Y @ ( sup_sup_set_state @ X2 @ Y ) ) ).
% sup_ge2
thf(fact_716_le__supI1,axiom,
! [X2: state > state > $o,A2: state > state > $o,B3: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ X2 @ A2 )
=> ( ord_le4344933087531911346tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ).
% le_supI1
thf(fact_717_le__supI1,axiom,
! [X2: $o > set_state,A2: $o > set_state,B3: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ A2 )
=> ( ord_le9189382018855386905_state @ X2 @ ( sup_sup_o_set_state @ A2 @ B3 ) ) ) ).
% le_supI1
thf(fact_718_le__supI1,axiom,
! [X2: set_set_state,A2: set_set_state,B3: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ A2 )
=> ( ord_le5175021213330142598_state @ X2 @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ).
% le_supI1
thf(fact_719_le__supI1,axiom,
! [X2: set_state,A2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ A2 )
=> ( ord_le2494988322063910608_state @ X2 @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ).
% le_supI1
thf(fact_720_le__supI2,axiom,
! [X2: state > state > $o,B3: state > state > $o,A2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ X2 @ B3 )
=> ( ord_le4344933087531911346tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ).
% le_supI2
thf(fact_721_le__supI2,axiom,
! [X2: $o > set_state,B3: $o > set_state,A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ B3 )
=> ( ord_le9189382018855386905_state @ X2 @ ( sup_sup_o_set_state @ A2 @ B3 ) ) ) ).
% le_supI2
thf(fact_722_le__supI2,axiom,
! [X2: set_set_state,B3: set_set_state,A2: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ B3 )
=> ( ord_le5175021213330142598_state @ X2 @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ).
% le_supI2
thf(fact_723_le__supI2,axiom,
! [X2: set_state,B3: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ B3 )
=> ( ord_le2494988322063910608_state @ X2 @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ).
% le_supI2
thf(fact_724_sup_Omono,axiom,
! [C: state > state > $o,A2: state > state > $o,D: state > state > $o,B3: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ C @ A2 )
=> ( ( ord_le4344933087531911346tate_o @ D @ B3 )
=> ( ord_le4344933087531911346tate_o @ ( sup_su7525921995284788454tate_o @ C @ D ) @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ) ).
% sup.mono
thf(fact_725_sup_Omono,axiom,
! [C: $o > set_state,A2: $o > set_state,D: $o > set_state,B3: $o > set_state] :
( ( ord_le9189382018855386905_state @ C @ A2 )
=> ( ( ord_le9189382018855386905_state @ D @ B3 )
=> ( ord_le9189382018855386905_state @ ( sup_sup_o_set_state @ C @ D ) @ ( sup_sup_o_set_state @ A2 @ B3 ) ) ) ) ).
% sup.mono
thf(fact_726_sup_Omono,axiom,
! [C: set_set_state,A2: set_set_state,D: set_set_state,B3: set_set_state] :
( ( ord_le5175021213330142598_state @ C @ A2 )
=> ( ( ord_le5175021213330142598_state @ D @ B3 )
=> ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ C @ D ) @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ) ).
% sup.mono
thf(fact_727_sup_Omono,axiom,
! [C: set_state,A2: set_state,D: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ C @ A2 )
=> ( ( ord_le2494988322063910608_state @ D @ B3 )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ C @ D ) @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ) ).
% sup.mono
thf(fact_728_sup__mono,axiom,
! [A2: state > state > $o,C: state > state > $o,B3: state > state > $o,D: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ A2 @ C )
=> ( ( ord_le4344933087531911346tate_o @ B3 @ D )
=> ( ord_le4344933087531911346tate_o @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) @ ( sup_su7525921995284788454tate_o @ C @ D ) ) ) ) ).
% sup_mono
thf(fact_729_sup__mono,axiom,
! [A2: $o > set_state,C: $o > set_state,B3: $o > set_state,D: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ C )
=> ( ( ord_le9189382018855386905_state @ B3 @ D )
=> ( ord_le9189382018855386905_state @ ( sup_sup_o_set_state @ A2 @ B3 ) @ ( sup_sup_o_set_state @ C @ D ) ) ) ) ).
% sup_mono
thf(fact_730_sup__mono,axiom,
! [A2: set_set_state,C: set_set_state,B3: set_set_state,D: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ C )
=> ( ( ord_le5175021213330142598_state @ B3 @ D )
=> ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ A2 @ B3 ) @ ( sup_su4188871578264421970_state @ C @ D ) ) ) ) ).
% sup_mono
thf(fact_731_sup__mono,axiom,
! [A2: set_state,C: set_state,B3: set_state,D: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ C )
=> ( ( ord_le2494988322063910608_state @ B3 @ D )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A2 @ B3 ) @ ( sup_sup_set_state @ C @ D ) ) ) ) ).
% sup_mono
thf(fact_732_sup__least,axiom,
! [Y: state > state > $o,X2: state > state > $o,Z2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ Y @ X2 )
=> ( ( ord_le4344933087531911346tate_o @ Z2 @ X2 )
=> ( ord_le4344933087531911346tate_o @ ( sup_su7525921995284788454tate_o @ Y @ Z2 ) @ X2 ) ) ) ).
% sup_least
thf(fact_733_sup__least,axiom,
! [Y: $o > set_state,X2: $o > set_state,Z2: $o > set_state] :
( ( ord_le9189382018855386905_state @ Y @ X2 )
=> ( ( ord_le9189382018855386905_state @ Z2 @ X2 )
=> ( ord_le9189382018855386905_state @ ( sup_sup_o_set_state @ Y @ Z2 ) @ X2 ) ) ) ).
% sup_least
thf(fact_734_sup__least,axiom,
! [Y: set_set_state,X2: set_set_state,Z2: set_set_state] :
( ( ord_le5175021213330142598_state @ Y @ X2 )
=> ( ( ord_le5175021213330142598_state @ Z2 @ X2 )
=> ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ Y @ Z2 ) @ X2 ) ) ) ).
% sup_least
thf(fact_735_sup__least,axiom,
! [Y: set_state,X2: set_state,Z2: set_state] :
( ( ord_le2494988322063910608_state @ Y @ X2 )
=> ( ( ord_le2494988322063910608_state @ Z2 @ X2 )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ Y @ Z2 ) @ X2 ) ) ) ).
% sup_least
thf(fact_736_le__iff__sup,axiom,
( ord_le4344933087531911346tate_o
= ( ^ [X3: state > state > $o,Y4: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ X3 @ Y4 )
= Y4 ) ) ) ).
% le_iff_sup
thf(fact_737_le__iff__sup,axiom,
( ord_le9189382018855386905_state
= ( ^ [X3: $o > set_state,Y4: $o > set_state] :
( ( sup_sup_o_set_state @ X3 @ Y4 )
= Y4 ) ) ) ).
% le_iff_sup
thf(fact_738_le__iff__sup,axiom,
( ord_le5175021213330142598_state
= ( ^ [X3: set_set_state,Y4: set_set_state] :
( ( sup_su4188871578264421970_state @ X3 @ Y4 )
= Y4 ) ) ) ).
% le_iff_sup
thf(fact_739_le__iff__sup,axiom,
( ord_le2494988322063910608_state
= ( ^ [X3: set_state,Y4: set_state] :
( ( sup_sup_set_state @ X3 @ Y4 )
= Y4 ) ) ) ).
% le_iff_sup
thf(fact_740_sup_OorderE,axiom,
! [B3: state > state > $o,A2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ B3 @ A2 )
=> ( A2
= ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ).
% sup.orderE
thf(fact_741_sup_OorderE,axiom,
! [B3: $o > set_state,A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ B3 @ A2 )
=> ( A2
= ( sup_sup_o_set_state @ A2 @ B3 ) ) ) ).
% sup.orderE
thf(fact_742_sup_OorderE,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( ord_le5175021213330142598_state @ B3 @ A2 )
=> ( A2
= ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ).
% sup.orderE
thf(fact_743_sup_OorderE,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ( A2
= ( sup_sup_set_state @ A2 @ B3 ) ) ) ).
% sup.orderE
thf(fact_744_sup_OorderI,axiom,
! [A2: state > state > $o,B3: state > state > $o] :
( ( A2
= ( sup_su7525921995284788454tate_o @ A2 @ B3 ) )
=> ( ord_le4344933087531911346tate_o @ B3 @ A2 ) ) ).
% sup.orderI
thf(fact_745_sup_OorderI,axiom,
! [A2: $o > set_state,B3: $o > set_state] :
( ( A2
= ( sup_sup_o_set_state @ A2 @ B3 ) )
=> ( ord_le9189382018855386905_state @ B3 @ A2 ) ) ).
% sup.orderI
thf(fact_746_sup_OorderI,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( A2
= ( sup_su4188871578264421970_state @ A2 @ B3 ) )
=> ( ord_le5175021213330142598_state @ B3 @ A2 ) ) ).
% sup.orderI
thf(fact_747_sup_OorderI,axiom,
! [A2: set_state,B3: set_state] :
( ( A2
= ( sup_sup_set_state @ A2 @ B3 ) )
=> ( ord_le2494988322063910608_state @ B3 @ A2 ) ) ).
% sup.orderI
thf(fact_748_sup__unique,axiom,
! [F: ( state > state > $o ) > ( state > state > $o ) > state > state > $o,X2: state > state > $o,Y: state > state > $o] :
( ! [X: state > state > $o,Y2: state > state > $o] : ( ord_le4344933087531911346tate_o @ X @ ( F @ X @ Y2 ) )
=> ( ! [X: state > state > $o,Y2: state > state > $o] : ( ord_le4344933087531911346tate_o @ Y2 @ ( F @ X @ Y2 ) )
=> ( ! [X: state > state > $o,Y2: state > state > $o,Z3: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ Y2 @ X )
=> ( ( ord_le4344933087531911346tate_o @ Z3 @ X )
=> ( ord_le4344933087531911346tate_o @ ( F @ Y2 @ Z3 ) @ X ) ) )
=> ( ( sup_su7525921995284788454tate_o @ X2 @ Y )
= ( F @ X2 @ Y ) ) ) ) ) ).
% sup_unique
thf(fact_749_sup__unique,axiom,
! [F: ( $o > set_state ) > ( $o > set_state ) > $o > set_state,X2: $o > set_state,Y: $o > set_state] :
( ! [X: $o > set_state,Y2: $o > set_state] : ( ord_le9189382018855386905_state @ X @ ( F @ X @ Y2 ) )
=> ( ! [X: $o > set_state,Y2: $o > set_state] : ( ord_le9189382018855386905_state @ Y2 @ ( F @ X @ Y2 ) )
=> ( ! [X: $o > set_state,Y2: $o > set_state,Z3: $o > set_state] :
( ( ord_le9189382018855386905_state @ Y2 @ X )
=> ( ( ord_le9189382018855386905_state @ Z3 @ X )
=> ( ord_le9189382018855386905_state @ ( F @ Y2 @ Z3 ) @ X ) ) )
=> ( ( sup_sup_o_set_state @ X2 @ Y )
= ( F @ X2 @ Y ) ) ) ) ) ).
% sup_unique
thf(fact_750_sup__unique,axiom,
! [F: set_set_state > set_set_state > set_set_state,X2: set_set_state,Y: set_set_state] :
( ! [X: set_set_state,Y2: set_set_state] : ( ord_le5175021213330142598_state @ X @ ( F @ X @ Y2 ) )
=> ( ! [X: set_set_state,Y2: set_set_state] : ( ord_le5175021213330142598_state @ Y2 @ ( F @ X @ Y2 ) )
=> ( ! [X: set_set_state,Y2: set_set_state,Z3: set_set_state] :
( ( ord_le5175021213330142598_state @ Y2 @ X )
=> ( ( ord_le5175021213330142598_state @ Z3 @ X )
=> ( ord_le5175021213330142598_state @ ( F @ Y2 @ Z3 ) @ X ) ) )
=> ( ( sup_su4188871578264421970_state @ X2 @ Y )
= ( F @ X2 @ Y ) ) ) ) ) ).
% sup_unique
thf(fact_751_sup__unique,axiom,
! [F: set_state > set_state > set_state,X2: set_state,Y: set_state] :
( ! [X: set_state,Y2: set_state] : ( ord_le2494988322063910608_state @ X @ ( F @ X @ Y2 ) )
=> ( ! [X: set_state,Y2: set_state] : ( ord_le2494988322063910608_state @ Y2 @ ( F @ X @ Y2 ) )
=> ( ! [X: set_state,Y2: set_state,Z3: set_state] :
( ( ord_le2494988322063910608_state @ Y2 @ X )
=> ( ( ord_le2494988322063910608_state @ Z3 @ X )
=> ( ord_le2494988322063910608_state @ ( F @ Y2 @ Z3 ) @ X ) ) )
=> ( ( sup_sup_set_state @ X2 @ Y )
= ( F @ X2 @ Y ) ) ) ) ) ).
% sup_unique
thf(fact_752_sup_Oabsorb1,axiom,
! [B3: state > state > $o,A2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ B3 @ A2 )
=> ( ( sup_su7525921995284788454tate_o @ A2 @ B3 )
= A2 ) ) ).
% sup.absorb1
thf(fact_753_sup_Oabsorb1,axiom,
! [B3: $o > set_state,A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ B3 @ A2 )
=> ( ( sup_sup_o_set_state @ A2 @ B3 )
= A2 ) ) ).
% sup.absorb1
thf(fact_754_sup_Oabsorb1,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( ord_le5175021213330142598_state @ B3 @ A2 )
=> ( ( sup_su4188871578264421970_state @ A2 @ B3 )
= A2 ) ) ).
% sup.absorb1
thf(fact_755_sup_Oabsorb1,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ( ( sup_sup_set_state @ A2 @ B3 )
= A2 ) ) ).
% sup.absorb1
thf(fact_756_sup_Oabsorb2,axiom,
! [A2: state > state > $o,B3: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ A2 @ B3 )
=> ( ( sup_su7525921995284788454tate_o @ A2 @ B3 )
= B3 ) ) ).
% sup.absorb2
thf(fact_757_sup_Oabsorb2,axiom,
! [A2: $o > set_state,B3: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ B3 )
=> ( ( sup_sup_o_set_state @ A2 @ B3 )
= B3 ) ) ).
% sup.absorb2
thf(fact_758_sup_Oabsorb2,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ B3 )
=> ( ( sup_su4188871578264421970_state @ A2 @ B3 )
= B3 ) ) ).
% sup.absorb2
thf(fact_759_sup_Oabsorb2,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( sup_sup_set_state @ A2 @ B3 )
= B3 ) ) ).
% sup.absorb2
thf(fact_760_sup__absorb1,axiom,
! [Y: state > state > $o,X2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ Y @ X2 )
=> ( ( sup_su7525921995284788454tate_o @ X2 @ Y )
= X2 ) ) ).
% sup_absorb1
thf(fact_761_sup__absorb1,axiom,
! [Y: $o > set_state,X2: $o > set_state] :
( ( ord_le9189382018855386905_state @ Y @ X2 )
=> ( ( sup_sup_o_set_state @ X2 @ Y )
= X2 ) ) ).
% sup_absorb1
thf(fact_762_sup__absorb1,axiom,
! [Y: set_set_state,X2: set_set_state] :
( ( ord_le5175021213330142598_state @ Y @ X2 )
=> ( ( sup_su4188871578264421970_state @ X2 @ Y )
= X2 ) ) ).
% sup_absorb1
thf(fact_763_sup__absorb1,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_le2494988322063910608_state @ Y @ X2 )
=> ( ( sup_sup_set_state @ X2 @ Y )
= X2 ) ) ).
% sup_absorb1
thf(fact_764_sup__absorb2,axiom,
! [X2: state > state > $o,Y: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ X2 @ Y )
=> ( ( sup_su7525921995284788454tate_o @ X2 @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_765_sup__absorb2,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ Y )
=> ( ( sup_sup_o_set_state @ X2 @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_766_sup__absorb2,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ Y )
=> ( ( sup_su4188871578264421970_state @ X2 @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_767_sup__absorb2,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( sup_sup_set_state @ X2 @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_768_sup_OboundedE,axiom,
! [B3: state > state > $o,C: state > state > $o,A2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ ( sup_su7525921995284788454tate_o @ B3 @ C ) @ A2 )
=> ~ ( ( ord_le4344933087531911346tate_o @ B3 @ A2 )
=> ~ ( ord_le4344933087531911346tate_o @ C @ A2 ) ) ) ).
% sup.boundedE
thf(fact_769_sup_OboundedE,axiom,
! [B3: $o > set_state,C: $o > set_state,A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ ( sup_sup_o_set_state @ B3 @ C ) @ A2 )
=> ~ ( ( ord_le9189382018855386905_state @ B3 @ A2 )
=> ~ ( ord_le9189382018855386905_state @ C @ A2 ) ) ) ).
% sup.boundedE
thf(fact_770_sup_OboundedE,axiom,
! [B3: set_set_state,C: set_set_state,A2: set_set_state] :
( ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ B3 @ C ) @ A2 )
=> ~ ( ( ord_le5175021213330142598_state @ B3 @ A2 )
=> ~ ( ord_le5175021213330142598_state @ C @ A2 ) ) ) ).
% sup.boundedE
thf(fact_771_sup_OboundedE,axiom,
! [B3: set_state,C: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B3 @ C ) @ A2 )
=> ~ ( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ~ ( ord_le2494988322063910608_state @ C @ A2 ) ) ) ).
% sup.boundedE
thf(fact_772_sup_OboundedI,axiom,
! [B3: state > state > $o,A2: state > state > $o,C: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ B3 @ A2 )
=> ( ( ord_le4344933087531911346tate_o @ C @ A2 )
=> ( ord_le4344933087531911346tate_o @ ( sup_su7525921995284788454tate_o @ B3 @ C ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_773_sup_OboundedI,axiom,
! [B3: $o > set_state,A2: $o > set_state,C: $o > set_state] :
( ( ord_le9189382018855386905_state @ B3 @ A2 )
=> ( ( ord_le9189382018855386905_state @ C @ A2 )
=> ( ord_le9189382018855386905_state @ ( sup_sup_o_set_state @ B3 @ C ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_774_sup_OboundedI,axiom,
! [B3: set_set_state,A2: set_set_state,C: set_set_state] :
( ( ord_le5175021213330142598_state @ B3 @ A2 )
=> ( ( ord_le5175021213330142598_state @ C @ A2 )
=> ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ B3 @ C ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_775_sup_OboundedI,axiom,
! [B3: set_state,A2: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ( ( ord_le2494988322063910608_state @ C @ A2 )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ B3 @ C ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_776_sup_Oorder__iff,axiom,
( ord_le4344933087531911346tate_o
= ( ^ [B4: state > state > $o,A4: state > state > $o] :
( A4
= ( sup_su7525921995284788454tate_o @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_777_sup_Oorder__iff,axiom,
( ord_le9189382018855386905_state
= ( ^ [B4: $o > set_state,A4: $o > set_state] :
( A4
= ( sup_sup_o_set_state @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_778_sup_Oorder__iff,axiom,
( ord_le5175021213330142598_state
= ( ^ [B4: set_set_state,A4: set_set_state] :
( A4
= ( sup_su4188871578264421970_state @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_779_sup_Oorder__iff,axiom,
( ord_le2494988322063910608_state
= ( ^ [B4: set_state,A4: set_state] :
( A4
= ( sup_sup_set_state @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_780_sup_Ocobounded1,axiom,
! [A2: state > state > $o,B3: state > state > $o] : ( ord_le4344933087531911346tate_o @ A2 @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_781_sup_Ocobounded1,axiom,
! [A2: $o > set_state,B3: $o > set_state] : ( ord_le9189382018855386905_state @ A2 @ ( sup_sup_o_set_state @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_782_sup_Ocobounded1,axiom,
! [A2: set_set_state,B3: set_set_state] : ( ord_le5175021213330142598_state @ A2 @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_783_sup_Ocobounded1,axiom,
! [A2: set_state,B3: set_state] : ( ord_le2494988322063910608_state @ A2 @ ( sup_sup_set_state @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_784_sup_Ocobounded2,axiom,
! [B3: state > state > $o,A2: state > state > $o] : ( ord_le4344933087531911346tate_o @ B3 @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_785_sup_Ocobounded2,axiom,
! [B3: $o > set_state,A2: $o > set_state] : ( ord_le9189382018855386905_state @ B3 @ ( sup_sup_o_set_state @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_786_sup_Ocobounded2,axiom,
! [B3: set_set_state,A2: set_set_state] : ( ord_le5175021213330142598_state @ B3 @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_787_sup_Ocobounded2,axiom,
! [B3: set_state,A2: set_state] : ( ord_le2494988322063910608_state @ B3 @ ( sup_sup_set_state @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_788_sup_Oabsorb__iff1,axiom,
( ord_le4344933087531911346tate_o
= ( ^ [B4: state > state > $o,A4: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_789_sup_Oabsorb__iff1,axiom,
( ord_le9189382018855386905_state
= ( ^ [B4: $o > set_state,A4: $o > set_state] :
( ( sup_sup_o_set_state @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_790_sup_Oabsorb__iff1,axiom,
( ord_le5175021213330142598_state
= ( ^ [B4: set_set_state,A4: set_set_state] :
( ( sup_su4188871578264421970_state @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_791_sup_Oabsorb__iff1,axiom,
( ord_le2494988322063910608_state
= ( ^ [B4: set_state,A4: set_state] :
( ( sup_sup_set_state @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_792_sup_Oabsorb__iff2,axiom,
( ord_le4344933087531911346tate_o
= ( ^ [A4: state > state > $o,B4: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_793_sup_Oabsorb__iff2,axiom,
( ord_le9189382018855386905_state
= ( ^ [A4: $o > set_state,B4: $o > set_state] :
( ( sup_sup_o_set_state @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_794_sup_Oabsorb__iff2,axiom,
( ord_le5175021213330142598_state
= ( ^ [A4: set_set_state,B4: set_set_state] :
( ( sup_su4188871578264421970_state @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_795_sup_Oabsorb__iff2,axiom,
( ord_le2494988322063910608_state
= ( ^ [A4: set_state,B4: set_state] :
( ( sup_sup_set_state @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_796_sup_OcoboundedI1,axiom,
! [C: state > state > $o,A2: state > state > $o,B3: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ C @ A2 )
=> ( ord_le4344933087531911346tate_o @ C @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_797_sup_OcoboundedI1,axiom,
! [C: $o > set_state,A2: $o > set_state,B3: $o > set_state] :
( ( ord_le9189382018855386905_state @ C @ A2 )
=> ( ord_le9189382018855386905_state @ C @ ( sup_sup_o_set_state @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_798_sup_OcoboundedI1,axiom,
! [C: set_set_state,A2: set_set_state,B3: set_set_state] :
( ( ord_le5175021213330142598_state @ C @ A2 )
=> ( ord_le5175021213330142598_state @ C @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_799_sup_OcoboundedI1,axiom,
! [C: set_state,A2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ C @ A2 )
=> ( ord_le2494988322063910608_state @ C @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_800_sup_OcoboundedI2,axiom,
! [C: state > state > $o,B3: state > state > $o,A2: state > state > $o] :
( ( ord_le4344933087531911346tate_o @ C @ B3 )
=> ( ord_le4344933087531911346tate_o @ C @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_801_sup_OcoboundedI2,axiom,
! [C: $o > set_state,B3: $o > set_state,A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ C @ B3 )
=> ( ord_le9189382018855386905_state @ C @ ( sup_sup_o_set_state @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_802_sup_OcoboundedI2,axiom,
! [C: set_set_state,B3: set_set_state,A2: set_set_state] :
( ( ord_le5175021213330142598_state @ C @ B3 )
=> ( ord_le5175021213330142598_state @ C @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_803_sup_OcoboundedI2,axiom,
! [C: set_state,B3: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ C @ B3 )
=> ( ord_le2494988322063910608_state @ C @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_804_bot_Oextremum,axiom,
! [A2: $o > set_state] : ( ord_le9189382018855386905_state @ bot_bot_o_set_state @ A2 ) ).
% bot.extremum
thf(fact_805_bot_Oextremum,axiom,
! [A2: set_set_state] : ( ord_le5175021213330142598_state @ bot_bo2271482359692755898_state @ A2 ) ).
% bot.extremum
thf(fact_806_bot_Oextremum,axiom,
! [A2: set_state] : ( ord_le2494988322063910608_state @ bot_bot_set_state @ A2 ) ).
% bot.extremum
thf(fact_807_bot_Oextremum__unique,axiom,
! [A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ bot_bot_o_set_state )
= ( A2 = bot_bot_o_set_state ) ) ).
% bot.extremum_unique
thf(fact_808_bot_Oextremum__unique,axiom,
! [A2: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ bot_bo2271482359692755898_state )
= ( A2 = bot_bo2271482359692755898_state ) ) ).
% bot.extremum_unique
thf(fact_809_bot_Oextremum__unique,axiom,
! [A2: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ bot_bot_set_state )
= ( A2 = bot_bot_set_state ) ) ).
% bot.extremum_unique
thf(fact_810_bot_Oextremum__uniqueI,axiom,
! [A2: $o > set_state] :
( ( ord_le9189382018855386905_state @ A2 @ bot_bot_o_set_state )
=> ( A2 = bot_bot_o_set_state ) ) ).
% bot.extremum_uniqueI
thf(fact_811_bot_Oextremum__uniqueI,axiom,
! [A2: set_set_state] :
( ( ord_le5175021213330142598_state @ A2 @ bot_bo2271482359692755898_state )
=> ( A2 = bot_bo2271482359692755898_state ) ) ).
% bot.extremum_uniqueI
thf(fact_812_bot_Oextremum__uniqueI,axiom,
! [A2: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ bot_bot_set_state )
=> ( A2 = bot_bot_set_state ) ) ).
% bot.extremum_uniqueI
thf(fact_813_sup_Ostrict__coboundedI2,axiom,
! [C: state > state > $o,B3: state > state > $o,A2: state > state > $o] :
( ( ord_le9065008989417891262tate_o @ C @ B3 )
=> ( ord_le9065008989417891262tate_o @ C @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ).
% sup.strict_coboundedI2
thf(fact_814_sup_Ostrict__coboundedI2,axiom,
! [C: set_state,B3: set_state,A2: set_state] :
( ( ord_less_set_state @ C @ B3 )
=> ( ord_less_set_state @ C @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ).
% sup.strict_coboundedI2
thf(fact_815_sup_Ostrict__coboundedI2,axiom,
! [C: set_set_state,B3: set_set_state,A2: set_set_state] :
( ( ord_le8280034978549525370_state @ C @ B3 )
=> ( ord_le8280034978549525370_state @ C @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ).
% sup.strict_coboundedI2
thf(fact_816_sup_Ostrict__coboundedI1,axiom,
! [C: state > state > $o,A2: state > state > $o,B3: state > state > $o] :
( ( ord_le9065008989417891262tate_o @ C @ A2 )
=> ( ord_le9065008989417891262tate_o @ C @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ).
% sup.strict_coboundedI1
thf(fact_817_sup_Ostrict__coboundedI1,axiom,
! [C: set_state,A2: set_state,B3: set_state] :
( ( ord_less_set_state @ C @ A2 )
=> ( ord_less_set_state @ C @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ).
% sup.strict_coboundedI1
thf(fact_818_sup_Ostrict__coboundedI1,axiom,
! [C: set_set_state,A2: set_set_state,B3: set_set_state] :
( ( ord_le8280034978549525370_state @ C @ A2 )
=> ( ord_le8280034978549525370_state @ C @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ).
% sup.strict_coboundedI1
thf(fact_819_sup_Ostrict__order__iff,axiom,
( ord_le9065008989417891262tate_o
= ( ^ [B4: state > state > $o,A4: state > state > $o] :
( ( A4
= ( sup_su7525921995284788454tate_o @ A4 @ B4 ) )
& ( A4 != B4 ) ) ) ) ).
% sup.strict_order_iff
thf(fact_820_sup_Ostrict__order__iff,axiom,
( ord_less_set_state
= ( ^ [B4: set_state,A4: set_state] :
( ( A4
= ( sup_sup_set_state @ A4 @ B4 ) )
& ( A4 != B4 ) ) ) ) ).
% sup.strict_order_iff
thf(fact_821_sup_Ostrict__order__iff,axiom,
( ord_le8280034978549525370_state
= ( ^ [B4: set_set_state,A4: set_set_state] :
( ( A4
= ( sup_su4188871578264421970_state @ A4 @ B4 ) )
& ( A4 != B4 ) ) ) ) ).
% sup.strict_order_iff
thf(fact_822_sup_Ostrict__boundedE,axiom,
! [B3: state > state > $o,C: state > state > $o,A2: state > state > $o] :
( ( ord_le9065008989417891262tate_o @ ( sup_su7525921995284788454tate_o @ B3 @ C ) @ A2 )
=> ~ ( ( ord_le9065008989417891262tate_o @ B3 @ A2 )
=> ~ ( ord_le9065008989417891262tate_o @ C @ A2 ) ) ) ).
% sup.strict_boundedE
thf(fact_823_sup_Ostrict__boundedE,axiom,
! [B3: set_state,C: set_state,A2: set_state] :
( ( ord_less_set_state @ ( sup_sup_set_state @ B3 @ C ) @ A2 )
=> ~ ( ( ord_less_set_state @ B3 @ A2 )
=> ~ ( ord_less_set_state @ C @ A2 ) ) ) ).
% sup.strict_boundedE
thf(fact_824_sup_Ostrict__boundedE,axiom,
! [B3: set_set_state,C: set_set_state,A2: set_set_state] :
( ( ord_le8280034978549525370_state @ ( sup_su4188871578264421970_state @ B3 @ C ) @ A2 )
=> ~ ( ( ord_le8280034978549525370_state @ B3 @ A2 )
=> ~ ( ord_le8280034978549525370_state @ C @ A2 ) ) ) ).
% sup.strict_boundedE
thf(fact_825_sup_Oabsorb4,axiom,
! [A2: state > state > $o,B3: state > state > $o] :
( ( ord_le9065008989417891262tate_o @ A2 @ B3 )
=> ( ( sup_su7525921995284788454tate_o @ A2 @ B3 )
= B3 ) ) ).
% sup.absorb4
thf(fact_826_sup_Oabsorb4,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_less_set_state @ A2 @ B3 )
=> ( ( sup_sup_set_state @ A2 @ B3 )
= B3 ) ) ).
% sup.absorb4
thf(fact_827_sup_Oabsorb4,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( ord_le8280034978549525370_state @ A2 @ B3 )
=> ( ( sup_su4188871578264421970_state @ A2 @ B3 )
= B3 ) ) ).
% sup.absorb4
thf(fact_828_sup_Oabsorb3,axiom,
! [B3: state > state > $o,A2: state > state > $o] :
( ( ord_le9065008989417891262tate_o @ B3 @ A2 )
=> ( ( sup_su7525921995284788454tate_o @ A2 @ B3 )
= A2 ) ) ).
% sup.absorb3
thf(fact_829_sup_Oabsorb3,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_less_set_state @ B3 @ A2 )
=> ( ( sup_sup_set_state @ A2 @ B3 )
= A2 ) ) ).
% sup.absorb3
thf(fact_830_sup_Oabsorb3,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( ord_le8280034978549525370_state @ B3 @ A2 )
=> ( ( sup_su4188871578264421970_state @ A2 @ B3 )
= A2 ) ) ).
% sup.absorb3
thf(fact_831_less__supI2,axiom,
! [X2: state > state > $o,B3: state > state > $o,A2: state > state > $o] :
( ( ord_le9065008989417891262tate_o @ X2 @ B3 )
=> ( ord_le9065008989417891262tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ).
% less_supI2
thf(fact_832_less__supI2,axiom,
! [X2: set_state,B3: set_state,A2: set_state] :
( ( ord_less_set_state @ X2 @ B3 )
=> ( ord_less_set_state @ X2 @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ).
% less_supI2
thf(fact_833_less__supI2,axiom,
! [X2: set_set_state,B3: set_set_state,A2: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ B3 )
=> ( ord_le8280034978549525370_state @ X2 @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ).
% less_supI2
thf(fact_834_less__supI1,axiom,
! [X2: state > state > $o,A2: state > state > $o,B3: state > state > $o] :
( ( ord_le9065008989417891262tate_o @ X2 @ A2 )
=> ( ord_le9065008989417891262tate_o @ X2 @ ( sup_su7525921995284788454tate_o @ A2 @ B3 ) ) ) ).
% less_supI1
thf(fact_835_less__supI1,axiom,
! [X2: set_state,A2: set_state,B3: set_state] :
( ( ord_less_set_state @ X2 @ A2 )
=> ( ord_less_set_state @ X2 @ ( sup_sup_set_state @ A2 @ B3 ) ) ) ).
% less_supI1
thf(fact_836_less__supI1,axiom,
! [X2: set_set_state,A2: set_set_state,B3: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ A2 )
=> ( ord_le8280034978549525370_state @ X2 @ ( sup_su4188871578264421970_state @ A2 @ B3 ) ) ) ).
% less_supI1
thf(fact_837_bot_Oextremum__strict,axiom,
! [A2: set_state] :
~ ( ord_less_set_state @ A2 @ bot_bot_set_state ) ).
% bot.extremum_strict
thf(fact_838_bot_Oextremum__strict,axiom,
! [A2: set_set_state] :
~ ( ord_le8280034978549525370_state @ A2 @ bot_bo2271482359692755898_state ) ).
% bot.extremum_strict
thf(fact_839_bot_Onot__eq__extremum,axiom,
! [A2: set_state] :
( ( A2 != bot_bot_set_state )
= ( ord_less_set_state @ bot_bot_set_state @ A2 ) ) ).
% bot.not_eq_extremum
thf(fact_840_bot_Onot__eq__extremum,axiom,
! [A2: set_set_state] :
( ( A2 != bot_bo2271482359692755898_state )
= ( ord_le8280034978549525370_state @ bot_bo2271482359692755898_state @ A2 ) ) ).
% bot.not_eq_extremum
thf(fact_841_Un__UNIV__left,axiom,
! [B: set_state] :
( ( sup_sup_set_state @ top_top_set_state @ B )
= top_top_set_state ) ).
% Un_UNIV_left
thf(fact_842_Un__UNIV__left,axiom,
! [B: set_set_state] :
( ( sup_su4188871578264421970_state @ top_to5262587396890829782_state @ B )
= top_to5262587396890829782_state ) ).
% Un_UNIV_left
thf(fact_843_Un__UNIV__right,axiom,
! [A: set_state] :
( ( sup_sup_set_state @ A @ top_top_set_state )
= top_top_set_state ) ).
% Un_UNIV_right
thf(fact_844_Un__UNIV__right,axiom,
! [A: set_set_state] :
( ( sup_su4188871578264421970_state @ A @ top_to5262587396890829782_state )
= top_to5262587396890829782_state ) ).
% Un_UNIV_right
thf(fact_845_Un__mono,axiom,
! [A: set_set_state,C2: set_set_state,B: set_set_state,D2: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ C2 )
=> ( ( ord_le5175021213330142598_state @ B @ D2 )
=> ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ A @ B ) @ ( sup_su4188871578264421970_state @ C2 @ D2 ) ) ) ) ).
% Un_mono
thf(fact_846_Un__mono,axiom,
! [A: set_state,C2: set_state,B: set_state,D2: set_state] :
( ( ord_le2494988322063910608_state @ A @ C2 )
=> ( ( ord_le2494988322063910608_state @ B @ D2 )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A @ B ) @ ( sup_sup_set_state @ C2 @ D2 ) ) ) ) ).
% Un_mono
thf(fact_847_Un__least,axiom,
! [A: set_set_state,C2: set_set_state,B: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ C2 )
=> ( ( ord_le5175021213330142598_state @ B @ C2 )
=> ( ord_le5175021213330142598_state @ ( sup_su4188871578264421970_state @ A @ B ) @ C2 ) ) ) ).
% Un_least
thf(fact_848_Un__least,axiom,
! [A: set_state,C2: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ C2 )
=> ( ( ord_le2494988322063910608_state @ B @ C2 )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ A @ B ) @ C2 ) ) ) ).
% Un_least
thf(fact_849_Un__upper1,axiom,
! [A: set_set_state,B: set_set_state] : ( ord_le5175021213330142598_state @ A @ ( sup_su4188871578264421970_state @ A @ B ) ) ).
% Un_upper1
thf(fact_850_Un__upper1,axiom,
! [A: set_state,B: set_state] : ( ord_le2494988322063910608_state @ A @ ( sup_sup_set_state @ A @ B ) ) ).
% Un_upper1
thf(fact_851_Un__upper2,axiom,
! [B: set_set_state,A: set_set_state] : ( ord_le5175021213330142598_state @ B @ ( sup_su4188871578264421970_state @ A @ B ) ) ).
% Un_upper2
thf(fact_852_Un__upper2,axiom,
! [B: set_state,A: set_state] : ( ord_le2494988322063910608_state @ B @ ( sup_sup_set_state @ A @ B ) ) ).
% Un_upper2
thf(fact_853_Un__absorb1,axiom,
! [A: set_set_state,B: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ B )
=> ( ( sup_su4188871578264421970_state @ A @ B )
= B ) ) ).
% Un_absorb1
thf(fact_854_Un__absorb1,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( sup_sup_set_state @ A @ B )
= B ) ) ).
% Un_absorb1
thf(fact_855_Un__absorb2,axiom,
! [B: set_set_state,A: set_set_state] :
( ( ord_le5175021213330142598_state @ B @ A )
=> ( ( sup_su4188871578264421970_state @ A @ B )
= A ) ) ).
% Un_absorb2
thf(fact_856_Un__absorb2,axiom,
! [B: set_state,A: set_state] :
( ( ord_le2494988322063910608_state @ B @ A )
=> ( ( sup_sup_set_state @ A @ B )
= A ) ) ).
% Un_absorb2
thf(fact_857_subset__UnE,axiom,
! [C2: set_set_state,A: set_set_state,B: set_set_state] :
( ( ord_le5175021213330142598_state @ C2 @ ( sup_su4188871578264421970_state @ A @ B ) )
=> ~ ! [A6: set_set_state] :
( ( ord_le5175021213330142598_state @ A6 @ A )
=> ! [B6: set_set_state] :
( ( ord_le5175021213330142598_state @ B6 @ B )
=> ( C2
!= ( sup_su4188871578264421970_state @ A6 @ B6 ) ) ) ) ) ).
% subset_UnE
thf(fact_858_subset__UnE,axiom,
! [C2: set_state,A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ C2 @ ( sup_sup_set_state @ A @ B ) )
=> ~ ! [A6: set_state] :
( ( ord_le2494988322063910608_state @ A6 @ A )
=> ! [B6: set_state] :
( ( ord_le2494988322063910608_state @ B6 @ B )
=> ( C2
!= ( sup_sup_set_state @ A6 @ B6 ) ) ) ) ) ).
% subset_UnE
thf(fact_859_subset__Un__eq,axiom,
( ord_le5175021213330142598_state
= ( ^ [A3: set_set_state,B2: set_set_state] :
( ( sup_su4188871578264421970_state @ A3 @ B2 )
= B2 ) ) ) ).
% subset_Un_eq
thf(fact_860_subset__Un__eq,axiom,
( ord_le2494988322063910608_state
= ( ^ [A3: set_state,B2: set_state] :
( ( sup_sup_set_state @ A3 @ B2 )
= B2 ) ) ) ).
% subset_Un_eq
thf(fact_861_empty__not__UNIV,axiom,
bot_bot_set_state != top_top_set_state ).
% empty_not_UNIV
thf(fact_862_empty__not__UNIV,axiom,
bot_bo2271482359692755898_state != top_to5262587396890829782_state ).
% empty_not_UNIV
thf(fact_863_not__psubset__empty,axiom,
! [A: set_state] :
~ ( ord_less_set_state @ A @ bot_bot_set_state ) ).
% not_psubset_empty
thf(fact_864_not__psubset__empty,axiom,
! [A: set_set_state] :
~ ( ord_le8280034978549525370_state @ A @ bot_bo2271482359692755898_state ) ).
% not_psubset_empty
thf(fact_865_not__empty__eq__Iic__eq__empty,axiom,
! [H: set_state] :
( bot_bo2271482359692755898_state
!= ( set_or5536065684288934121_state @ H ) ) ).
% not_empty_eq_Iic_eq_empty
thf(fact_866_not__empty__eq__Ici__eq__empty,axiom,
! [L: set_state] :
( bot_bo2271482359692755898_state
!= ( set_or6477372120337742821_state @ L ) ) ).
% not_empty_eq_Ici_eq_empty
thf(fact_867_pairwise__empty,axiom,
! [P: state > state > $o] : ( pairwise_state @ P @ bot_bot_set_state ) ).
% pairwise_empty
thf(fact_868_pairwise__empty,axiom,
! [P: set_state > set_state > $o] : ( pairwise_set_state @ P @ bot_bo2271482359692755898_state ) ).
% pairwise_empty
thf(fact_869_sup__cancel__left2,axiom,
! [X2: state > state > $o,A2: state > state > $o,B3: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ ( sup_su7525921995284788454tate_o @ ( uminus7723173452139699081tate_o @ X2 ) @ A2 ) @ ( sup_su7525921995284788454tate_o @ X2 @ B3 ) )
= top_to5868225466921797218tate_o ) ).
% sup_cancel_left2
thf(fact_870_sup__cancel__left2,axiom,
! [X2: state > $o,A2: state > $o,B3: state > $o] :
( ( sup_sup_state_o @ ( sup_sup_state_o @ ( uminus3809647891681718284tate_o @ X2 ) @ A2 ) @ ( sup_sup_state_o @ X2 @ B3 ) )
= top_top_state_o ) ).
% sup_cancel_left2
thf(fact_871_sup__cancel__left2,axiom,
! [X2: set_set_state,A2: set_set_state,B3: set_set_state] :
( ( sup_su4188871578264421970_state @ ( sup_su4188871578264421970_state @ ( uminus4035512285888117871_state @ X2 ) @ A2 ) @ ( sup_su4188871578264421970_state @ X2 @ B3 ) )
= top_to5262587396890829782_state ) ).
% sup_cancel_left2
thf(fact_872_sup__cancel__left2,axiom,
! [X2: set_state,A2: set_state,B3: set_state] :
( ( sup_sup_set_state @ ( sup_sup_set_state @ ( uminus472742206872269241_state @ X2 ) @ A2 ) @ ( sup_sup_set_state @ X2 @ B3 ) )
= top_top_set_state ) ).
% sup_cancel_left2
thf(fact_873_sup__cancel__left1,axiom,
! [X2: state > state > $o,A2: state > state > $o,B3: state > state > $o] :
( ( sup_su7525921995284788454tate_o @ ( sup_su7525921995284788454tate_o @ X2 @ A2 ) @ ( sup_su7525921995284788454tate_o @ ( uminus7723173452139699081tate_o @ X2 ) @ B3 ) )
= top_to5868225466921797218tate_o ) ).
% sup_cancel_left1
thf(fact_874_sup__cancel__left1,axiom,
! [X2: state > $o,A2: state > $o,B3: state > $o] :
( ( sup_sup_state_o @ ( sup_sup_state_o @ X2 @ A2 ) @ ( sup_sup_state_o @ ( uminus3809647891681718284tate_o @ X2 ) @ B3 ) )
= top_top_state_o ) ).
% sup_cancel_left1
thf(fact_875_sup__cancel__left1,axiom,
! [X2: set_set_state,A2: set_set_state,B3: set_set_state] :
( ( sup_su4188871578264421970_state @ ( sup_su4188871578264421970_state @ X2 @ A2 ) @ ( sup_su4188871578264421970_state @ ( uminus4035512285888117871_state @ X2 ) @ B3 ) )
= top_to5262587396890829782_state ) ).
% sup_cancel_left1
thf(fact_876_sup__cancel__left1,axiom,
! [X2: set_state,A2: set_state,B3: set_state] :
( ( sup_sup_set_state @ ( sup_sup_set_state @ X2 @ A2 ) @ ( sup_sup_set_state @ ( uminus472742206872269241_state @ X2 ) @ B3 ) )
= top_top_set_state ) ).
% sup_cancel_left1
thf(fact_877_atLeast__eq__UNIV__iff,axiom,
! [X2: set_set_state] :
( ( ( set_or922425460254742171_state @ X2 )
= top_to3598970937283095436_state )
= ( X2 = bot_bo2271482359692755898_state ) ) ).
% atLeast_eq_UNIV_iff
thf(fact_878_atLeast__eq__UNIV__iff,axiom,
! [X2: set_state] :
( ( ( set_or6477372120337742821_state @ X2 )
= top_to5262587396890829782_state )
= ( X2 = bot_bot_set_state ) ) ).
% atLeast_eq_UNIV_iff
thf(fact_879_Compl__partition,axiom,
! [A: set_set_state] :
( ( sup_su4188871578264421970_state @ A @ ( uminus4035512285888117871_state @ A ) )
= top_to5262587396890829782_state ) ).
% Compl_partition
thf(fact_880_Compl__partition,axiom,
! [A: set_state] :
( ( sup_sup_set_state @ A @ ( uminus472742206872269241_state @ A ) )
= top_top_set_state ) ).
% Compl_partition
thf(fact_881_Compl__partition2,axiom,
! [A: set_set_state] :
( ( sup_su4188871578264421970_state @ ( uminus4035512285888117871_state @ A ) @ A )
= top_to5262587396890829782_state ) ).
% Compl_partition2
thf(fact_882_Compl__partition2,axiom,
! [A: set_state] :
( ( sup_sup_set_state @ ( uminus472742206872269241_state @ A ) @ A )
= top_top_set_state ) ).
% Compl_partition2
thf(fact_883_Compl__UNIV__eq,axiom,
( ( uminus4035512285888117871_state @ top_to5262587396890829782_state )
= bot_bo2271482359692755898_state ) ).
% Compl_UNIV_eq
thf(fact_884_Compl__UNIV__eq,axiom,
( ( uminus472742206872269241_state @ top_top_set_state )
= bot_bot_set_state ) ).
% Compl_UNIV_eq
thf(fact_885_Compl__empty__eq,axiom,
( ( uminus4035512285888117871_state @ bot_bo2271482359692755898_state )
= top_to5262587396890829782_state ) ).
% Compl_empty_eq
thf(fact_886_Compl__empty__eq,axiom,
( ( uminus472742206872269241_state @ bot_bot_set_state )
= top_top_set_state ) ).
% Compl_empty_eq
thf(fact_887_subset__Compl__self__eq,axiom,
! [A: set_set_state] :
( ( ord_le5175021213330142598_state @ A @ ( uminus4035512285888117871_state @ A ) )
= ( A = bot_bo2271482359692755898_state ) ) ).
% subset_Compl_self_eq
thf(fact_888_subset__Compl__self__eq,axiom,
! [A: set_state] :
( ( ord_le2494988322063910608_state @ A @ ( uminus472742206872269241_state @ A ) )
= ( A = bot_bot_set_state ) ) ).
% subset_Compl_self_eq
thf(fact_889_sup__shunt,axiom,
! [X2: state > state > $o,Y: state > state > $o] :
( ( ( sup_su7525921995284788454tate_o @ X2 @ Y )
= top_to5868225466921797218tate_o )
= ( ord_le4344933087531911346tate_o @ ( uminus7723173452139699081tate_o @ X2 ) @ Y ) ) ).
% sup_shunt
thf(fact_890_sup__shunt,axiom,
! [X2: state > $o,Y: state > $o] :
( ( ( sup_sup_state_o @ X2 @ Y )
= top_top_state_o )
= ( ord_less_eq_state_o @ ( uminus3809647891681718284tate_o @ X2 ) @ Y ) ) ).
% sup_shunt
thf(fact_891_sup__shunt,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ( sup_sup_o_set_state @ X2 @ Y )
= top_top_o_set_state )
= ( ord_le9189382018855386905_state @ ( uminus4730887800166984048_state @ X2 ) @ Y ) ) ).
% sup_shunt
thf(fact_892_sup__shunt,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ( sup_su4188871578264421970_state @ X2 @ Y )
= top_to5262587396890829782_state )
= ( ord_le5175021213330142598_state @ ( uminus4035512285888117871_state @ X2 ) @ Y ) ) ).
% sup_shunt
thf(fact_893_sup__shunt,axiom,
! [X2: set_state,Y: set_state] :
( ( ( sup_sup_set_state @ X2 @ Y )
= top_top_set_state )
= ( ord_le2494988322063910608_state @ ( uminus472742206872269241_state @ X2 ) @ Y ) ) ).
% sup_shunt
thf(fact_894_atLeastAtMost__eq__UNIV__iff,axiom,
! [X2: state > $o,Y: state > $o] :
( ( ( set_or2467210022473197514tate_o @ X2 @ Y )
= top_top_set_state_o2 )
= ( ( X2 = bot_bot_state_o )
& ( Y = top_top_state_o ) ) ) ).
% atLeastAtMost_eq_UNIV_iff
thf(fact_895_atLeastAtMost__eq__UNIV__iff,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ( set_or7796883608616495921_state @ X2 @ Y )
= top_to3598970937283095436_state )
= ( ( X2 = bot_bo2271482359692755898_state )
& ( Y = top_to5262587396890829782_state ) ) ) ).
% atLeastAtMost_eq_UNIV_iff
thf(fact_896_atLeastAtMost__eq__UNIV__iff,axiom,
! [X2: set_state,Y: set_state] :
( ( ( set_or701696889746204795_state @ X2 @ Y )
= top_to5262587396890829782_state )
= ( ( X2 = bot_bot_set_state )
& ( Y = top_top_set_state ) ) ) ).
% atLeastAtMost_eq_UNIV_iff
thf(fact_897_subset__emptyI,axiom,
! [A: set_set_set_state] :
( ! [X: set_set_state] :
~ ( member_set_set_state @ X @ A )
=> ( ord_le3154822624800881980_state @ A @ bot_bo7389043141884672880_state ) ) ).
% subset_emptyI
thf(fact_898_subset__emptyI,axiom,
! [A: set_set_state] :
( ! [X: set_state] :
~ ( member_set_state @ X @ A )
=> ( ord_le5175021213330142598_state @ A @ bot_bo2271482359692755898_state ) ) ).
% subset_emptyI
thf(fact_899_subset__emptyI,axiom,
! [A: set_state] :
( ! [X: state] :
~ ( member_state @ X @ A )
=> ( ord_le2494988322063910608_state @ A @ bot_bot_set_state ) ) ).
% subset_emptyI
thf(fact_900_Set_Ois__empty__def,axiom,
( is_empty_state
= ( ^ [A3: set_state] : ( A3 = bot_bot_set_state ) ) ) ).
% Set.is_empty_def
thf(fact_901_Set_Ois__empty__def,axiom,
( is_empty_set_state
= ( ^ [A3: set_set_state] : ( A3 = bot_bo2271482359692755898_state ) ) ) ).
% Set.is_empty_def
thf(fact_902_Inf__atMostLessThan,axiom,
! [X2: state > $o] :
( ( ord_less_state_o @ top_top_state_o @ X2 )
=> ( ( comple6810834910230287260tate_o @ ( set_or3075120673672437176tate_o @ X2 ) )
= bot_bot_state_o ) ) ).
% Inf_atMostLessThan
thf(fact_903_Inf__atMostLessThan,axiom,
! [X2: set_set_state] :
( ( ord_le8280034978549525370_state @ top_to5262587396890829782_state @ X2 )
=> ( ( comple2682067033655477471_state @ ( set_or5856722414167211971_state @ X2 ) )
= bot_bo2271482359692755898_state ) ) ).
% Inf_atMostLessThan
thf(fact_904_Inf__atMostLessThan,axiom,
! [X2: set_state] :
( ( ord_less_set_state @ top_top_set_state @ X2 )
=> ( ( comple1177038664686533161_state @ ( set_or1034127368735114509_state @ X2 ) )
= bot_bot_set_state ) ) ).
% Inf_atMostLessThan
thf(fact_905_insert__absorb2,axiom,
! [X2: state,A: set_state] :
( ( insert_state @ X2 @ ( insert_state @ X2 @ A ) )
= ( insert_state @ X2 @ A ) ) ).
% insert_absorb2
thf(fact_906_insert__absorb2,axiom,
! [X2: set_state,A: set_set_state] :
( ( insert_set_state @ X2 @ ( insert_set_state @ X2 @ A ) )
= ( insert_set_state @ X2 @ A ) ) ).
% insert_absorb2
thf(fact_907_insert__iff,axiom,
! [A2: set_state,B3: set_state,A: set_set_state] :
( ( member_set_state @ A2 @ ( insert_set_state @ B3 @ A ) )
= ( ( A2 = B3 )
| ( member_set_state @ A2 @ A ) ) ) ).
% insert_iff
thf(fact_908_insert__iff,axiom,
! [A2: set_set_state,B3: set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ A2 @ ( insert_set_set_state @ B3 @ A ) )
= ( ( A2 = B3 )
| ( member_set_set_state @ A2 @ A ) ) ) ).
% insert_iff
thf(fact_909_insert__iff,axiom,
! [A2: state,B3: state,A: set_state] :
( ( member_state @ A2 @ ( insert_state @ B3 @ A ) )
= ( ( A2 = B3 )
| ( member_state @ A2 @ A ) ) ) ).
% insert_iff
thf(fact_910_insertCI,axiom,
! [A2: set_state,B: set_set_state,B3: set_state] :
( ( ~ ( member_set_state @ A2 @ B )
=> ( A2 = B3 ) )
=> ( member_set_state @ A2 @ ( insert_set_state @ B3 @ B ) ) ) ).
% insertCI
thf(fact_911_insertCI,axiom,
! [A2: set_set_state,B: set_set_set_state,B3: set_set_state] :
( ( ~ ( member_set_set_state @ A2 @ B )
=> ( A2 = B3 ) )
=> ( member_set_set_state @ A2 @ ( insert_set_set_state @ B3 @ B ) ) ) ).
% insertCI
thf(fact_912_insertCI,axiom,
! [A2: state,B: set_state,B3: state] :
( ( ~ ( member_state @ A2 @ B )
=> ( A2 = B3 ) )
=> ( member_state @ A2 @ ( insert_state @ B3 @ B ) ) ) ).
% insertCI
thf(fact_913_singletonI,axiom,
! [A2: set_set_state] : ( member_set_set_state @ A2 @ ( insert_set_set_state @ A2 @ bot_bo7389043141884672880_state ) ) ).
% singletonI
thf(fact_914_singletonI,axiom,
! [A2: set_state] : ( member_set_state @ A2 @ ( insert_set_state @ A2 @ bot_bo2271482359692755898_state ) ) ).
% singletonI
thf(fact_915_singletonI,axiom,
! [A2: state] : ( member_state @ A2 @ ( insert_state @ A2 @ bot_bot_set_state ) ) ).
% singletonI
thf(fact_916_insert__subset,axiom,
! [X2: set_set_state,A: set_set_set_state,B: set_set_set_state] :
( ( ord_le3154822624800881980_state @ ( insert_set_set_state @ X2 @ A ) @ B )
= ( ( member_set_set_state @ X2 @ B )
& ( ord_le3154822624800881980_state @ A @ B ) ) ) ).
% insert_subset
thf(fact_917_insert__subset,axiom,
! [X2: set_state,A: set_set_state,B: set_set_state] :
( ( ord_le5175021213330142598_state @ ( insert_set_state @ X2 @ A ) @ B )
= ( ( member_set_state @ X2 @ B )
& ( ord_le5175021213330142598_state @ A @ B ) ) ) ).
% insert_subset
thf(fact_918_insert__subset,axiom,
! [X2: state,A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ ( insert_state @ X2 @ A ) @ B )
= ( ( member_state @ X2 @ B )
& ( ord_le2494988322063910608_state @ A @ B ) ) ) ).
% insert_subset
thf(fact_919_Un__insert__right,axiom,
! [A: set_state,A2: state,B: set_state] :
( ( sup_sup_set_state @ A @ ( insert_state @ A2 @ B ) )
= ( insert_state @ A2 @ ( sup_sup_set_state @ A @ B ) ) ) ).
% Un_insert_right
thf(fact_920_Un__insert__right,axiom,
! [A: set_set_state,A2: set_state,B: set_set_state] :
( ( sup_su4188871578264421970_state @ A @ ( insert_set_state @ A2 @ B ) )
= ( insert_set_state @ A2 @ ( sup_su4188871578264421970_state @ A @ B ) ) ) ).
% Un_insert_right
thf(fact_921_Un__insert__left,axiom,
! [A2: state,B: set_state,C2: set_state] :
( ( sup_sup_set_state @ ( insert_state @ A2 @ B ) @ C2 )
= ( insert_state @ A2 @ ( sup_sup_set_state @ B @ C2 ) ) ) ).
% Un_insert_left
thf(fact_922_Un__insert__left,axiom,
! [A2: set_state,B: set_set_state,C2: set_set_state] :
( ( sup_su4188871578264421970_state @ ( insert_set_state @ A2 @ B ) @ C2 )
= ( insert_set_state @ A2 @ ( sup_su4188871578264421970_state @ B @ C2 ) ) ) ).
% Un_insert_left
thf(fact_923_cInf__atLeast,axiom,
! [X2: set_state] :
( ( comple1177038664686533161_state @ ( set_or6477372120337742821_state @ X2 ) )
= X2 ) ).
% cInf_atLeast
thf(fact_924_Inf__atLeast,axiom,
! [X2: set_state] :
( ( comple1177038664686533161_state @ ( set_or6477372120337742821_state @ X2 ) )
= X2 ) ).
% Inf_atLeast
thf(fact_925_singleton__insert__inj__eq_H,axiom,
! [A2: set_state,A: set_set_state,B3: set_state] :
( ( ( insert_set_state @ A2 @ A )
= ( insert_set_state @ B3 @ bot_bo2271482359692755898_state ) )
= ( ( A2 = B3 )
& ( ord_le5175021213330142598_state @ A @ ( insert_set_state @ B3 @ bot_bo2271482359692755898_state ) ) ) ) ).
% singleton_insert_inj_eq'
thf(fact_926_singleton__insert__inj__eq_H,axiom,
! [A2: state,A: set_state,B3: state] :
( ( ( insert_state @ A2 @ A )
= ( insert_state @ B3 @ bot_bot_set_state ) )
= ( ( A2 = B3 )
& ( ord_le2494988322063910608_state @ A @ ( insert_state @ B3 @ bot_bot_set_state ) ) ) ) ).
% singleton_insert_inj_eq'
thf(fact_927_singleton__insert__inj__eq,axiom,
! [B3: set_state,A2: set_state,A: set_set_state] :
( ( ( insert_set_state @ B3 @ bot_bo2271482359692755898_state )
= ( insert_set_state @ A2 @ A ) )
= ( ( A2 = B3 )
& ( ord_le5175021213330142598_state @ A @ ( insert_set_state @ B3 @ bot_bo2271482359692755898_state ) ) ) ) ).
% singleton_insert_inj_eq
thf(fact_928_singleton__insert__inj__eq,axiom,
! [B3: state,A2: state,A: set_state] :
( ( ( insert_state @ B3 @ bot_bot_set_state )
= ( insert_state @ A2 @ A ) )
= ( ( A2 = B3 )
& ( ord_le2494988322063910608_state @ A @ ( insert_state @ B3 @ bot_bot_set_state ) ) ) ) ).
% singleton_insert_inj_eq
thf(fact_929_cInf__atLeastAtMost,axiom,
! [Y: $o > set_state,X2: $o > set_state] :
( ( ord_le9189382018855386905_state @ Y @ X2 )
=> ( ( comple1470863462450220288_state @ ( set_or7399831441507084590_state @ Y @ X2 ) )
= Y ) ) ).
% cInf_atLeastAtMost
thf(fact_930_cInf__atLeastAtMost,axiom,
! [Y: set_set_state,X2: set_set_state] :
( ( ord_le5175021213330142598_state @ Y @ X2 )
=> ( ( comple2682067033655477471_state @ ( set_or7796883608616495921_state @ Y @ X2 ) )
= Y ) ) ).
% cInf_atLeastAtMost
thf(fact_931_cInf__atLeastAtMost,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_le2494988322063910608_state @ Y @ X2 )
=> ( ( comple1177038664686533161_state @ ( set_or701696889746204795_state @ Y @ X2 ) )
= Y ) ) ).
% cInf_atLeastAtMost
thf(fact_932_Inf__atLeastAtMost,axiom,
! [X2: $o > set_state,Y: $o > set_state] :
( ( ord_le9189382018855386905_state @ X2 @ Y )
=> ( ( comple1470863462450220288_state @ ( set_or7399831441507084590_state @ X2 @ Y ) )
= X2 ) ) ).
% Inf_atLeastAtMost
thf(fact_933_Inf__atLeastAtMost,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le5175021213330142598_state @ X2 @ Y )
=> ( ( comple2682067033655477471_state @ ( set_or7796883608616495921_state @ X2 @ Y ) )
= X2 ) ) ).
% Inf_atLeastAtMost
thf(fact_934_Inf__atLeastAtMost,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( comple1177038664686533161_state @ ( set_or701696889746204795_state @ X2 @ Y ) )
= X2 ) ) ).
% Inf_atLeastAtMost
thf(fact_935_cInf__singleton,axiom,
! [X2: set_state] :
( ( comple1177038664686533161_state @ ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) )
= X2 ) ).
% cInf_singleton
thf(fact_936_atLeastAtMost__singleton,axiom,
! [A2: set_state] :
( ( set_or701696889746204795_state @ A2 @ A2 )
= ( insert_set_state @ A2 @ bot_bo2271482359692755898_state ) ) ).
% atLeastAtMost_singleton
thf(fact_937_atLeastAtMost__singleton__iff,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ( set_or701696889746204795_state @ A2 @ B3 )
= ( insert_set_state @ C @ bot_bo2271482359692755898_state ) )
= ( ( A2 = B3 )
& ( B3 = C ) ) ) ).
% atLeastAtMost_singleton_iff
thf(fact_938_cInf__atLeastLessThan,axiom,
! [Y: set_set_state,X2: set_set_state] :
( ( ord_le8280034978549525370_state @ Y @ X2 )
=> ( ( comple2682067033655477471_state @ ( set_or5996981303281673813_state @ Y @ X2 ) )
= Y ) ) ).
% cInf_atLeastLessThan
thf(fact_939_cInf__atLeastLessThan,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_less_set_state @ Y @ X2 )
=> ( ( comple1177038664686533161_state @ ( set_or2838015025653527455_state @ Y @ X2 ) )
= Y ) ) ).
% cInf_atLeastLessThan
thf(fact_940_Inf__atLeastLessThan,axiom,
! [X2: set_set_state,Y: set_set_state] :
( ( ord_le8280034978549525370_state @ X2 @ Y )
=> ( ( comple2682067033655477471_state @ ( set_or5996981303281673813_state @ X2 @ Y ) )
= X2 ) ) ).
% Inf_atLeastLessThan
thf(fact_941_Inf__atLeastLessThan,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_less_set_state @ X2 @ Y )
=> ( ( comple1177038664686533161_state @ ( set_or2838015025653527455_state @ X2 @ Y ) )
= X2 ) ) ).
% Inf_atLeastLessThan
thf(fact_942_Inf__atMost,axiom,
! [X2: set_set_state] :
( ( comple2682067033655477471_state @ ( set_or8190520063335472031_state @ X2 ) )
= bot_bo2271482359692755898_state ) ).
% Inf_atMost
thf(fact_943_Inf__atMost,axiom,
! [X2: set_state] :
( ( comple1177038664686533161_state @ ( set_or5536065684288934121_state @ X2 ) )
= bot_bot_set_state ) ).
% Inf_atMost
thf(fact_944_subset__Compl__singleton,axiom,
! [A: set_set_set_state,B3: set_set_state] :
( ( ord_le3154822624800881980_state @ A @ ( uminus2384571021370171429_state @ ( insert_set_set_state @ B3 @ bot_bo7389043141884672880_state ) ) )
= ( ~ ( member_set_set_state @ B3 @ A ) ) ) ).
% subset_Compl_singleton
thf(fact_945_subset__Compl__singleton,axiom,
! [A: set_set_state,B3: set_state] :
( ( ord_le5175021213330142598_state @ A @ ( uminus4035512285888117871_state @ ( insert_set_state @ B3 @ bot_bo2271482359692755898_state ) ) )
= ( ~ ( member_set_state @ B3 @ A ) ) ) ).
% subset_Compl_singleton
thf(fact_946_subset__Compl__singleton,axiom,
! [A: set_state,B3: state] :
( ( ord_le2494988322063910608_state @ A @ ( uminus472742206872269241_state @ ( insert_state @ B3 @ bot_bot_set_state ) ) )
= ( ~ ( member_state @ B3 @ A ) ) ) ).
% subset_Compl_singleton
thf(fact_947_insert__subsetI,axiom,
! [X2: set_set_state,A: set_set_set_state,X5: set_set_set_state] :
( ( member_set_set_state @ X2 @ A )
=> ( ( ord_le3154822624800881980_state @ X5 @ A )
=> ( ord_le3154822624800881980_state @ ( insert_set_set_state @ X2 @ X5 ) @ A ) ) ) ).
% insert_subsetI
thf(fact_948_insert__subsetI,axiom,
! [X2: set_state,A: set_set_state,X5: set_set_state] :
( ( member_set_state @ X2 @ A )
=> ( ( ord_le5175021213330142598_state @ X5 @ A )
=> ( ord_le5175021213330142598_state @ ( insert_set_state @ X2 @ X5 ) @ A ) ) ) ).
% insert_subsetI
thf(fact_949_insert__subsetI,axiom,
! [X2: state,A: set_state,X5: set_state] :
( ( member_state @ X2 @ A )
=> ( ( ord_le2494988322063910608_state @ X5 @ A )
=> ( ord_le2494988322063910608_state @ ( insert_state @ X2 @ X5 ) @ A ) ) ) ).
% insert_subsetI
thf(fact_950_mk__disjoint__insert,axiom,
! [A2: set_state,A: set_set_state] :
( ( member_set_state @ A2 @ A )
=> ? [B7: set_set_state] :
( ( A
= ( insert_set_state @ A2 @ B7 ) )
& ~ ( member_set_state @ A2 @ B7 ) ) ) ).
% mk_disjoint_insert
thf(fact_951_mk__disjoint__insert,axiom,
! [A2: set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ A2 @ A )
=> ? [B7: set_set_set_state] :
( ( A
= ( insert_set_set_state @ A2 @ B7 ) )
& ~ ( member_set_set_state @ A2 @ B7 ) ) ) ).
% mk_disjoint_insert
thf(fact_952_mk__disjoint__insert,axiom,
! [A2: state,A: set_state] :
( ( member_state @ A2 @ A )
=> ? [B7: set_state] :
( ( A
= ( insert_state @ A2 @ B7 ) )
& ~ ( member_state @ A2 @ B7 ) ) ) ).
% mk_disjoint_insert
thf(fact_953_insert__commute,axiom,
! [X2: state,Y: state,A: set_state] :
( ( insert_state @ X2 @ ( insert_state @ Y @ A ) )
= ( insert_state @ Y @ ( insert_state @ X2 @ A ) ) ) ).
% insert_commute
thf(fact_954_insert__commute,axiom,
! [X2: set_state,Y: set_state,A: set_set_state] :
( ( insert_set_state @ X2 @ ( insert_set_state @ Y @ A ) )
= ( insert_set_state @ Y @ ( insert_set_state @ X2 @ A ) ) ) ).
% insert_commute
thf(fact_955_insert__eq__iff,axiom,
! [A2: set_state,A: set_set_state,B3: set_state,B: set_set_state] :
( ~ ( member_set_state @ A2 @ A )
=> ( ~ ( member_set_state @ B3 @ B )
=> ( ( ( insert_set_state @ A2 @ A )
= ( insert_set_state @ B3 @ B ) )
= ( ( ( A2 = B3 )
=> ( A = B ) )
& ( ( A2 != B3 )
=> ? [C5: set_set_state] :
( ( A
= ( insert_set_state @ B3 @ C5 ) )
& ~ ( member_set_state @ B3 @ C5 )
& ( B
= ( insert_set_state @ A2 @ C5 ) )
& ~ ( member_set_state @ A2 @ C5 ) ) ) ) ) ) ) ).
% insert_eq_iff
thf(fact_956_insert__eq__iff,axiom,
! [A2: set_set_state,A: set_set_set_state,B3: set_set_state,B: set_set_set_state] :
( ~ ( member_set_set_state @ A2 @ A )
=> ( ~ ( member_set_set_state @ B3 @ B )
=> ( ( ( insert_set_set_state @ A2 @ A )
= ( insert_set_set_state @ B3 @ B ) )
= ( ( ( A2 = B3 )
=> ( A = B ) )
& ( ( A2 != B3 )
=> ? [C5: set_set_set_state] :
( ( A
= ( insert_set_set_state @ B3 @ C5 ) )
& ~ ( member_set_set_state @ B3 @ C5 )
& ( B
= ( insert_set_set_state @ A2 @ C5 ) )
& ~ ( member_set_set_state @ A2 @ C5 ) ) ) ) ) ) ) ).
% insert_eq_iff
thf(fact_957_insert__eq__iff,axiom,
! [A2: state,A: set_state,B3: state,B: set_state] :
( ~ ( member_state @ A2 @ A )
=> ( ~ ( member_state @ B3 @ B )
=> ( ( ( insert_state @ A2 @ A )
= ( insert_state @ B3 @ B ) )
= ( ( ( A2 = B3 )
=> ( A = B ) )
& ( ( A2 != B3 )
=> ? [C5: set_state] :
( ( A
= ( insert_state @ B3 @ C5 ) )
& ~ ( member_state @ B3 @ C5 )
& ( B
= ( insert_state @ A2 @ C5 ) )
& ~ ( member_state @ A2 @ C5 ) ) ) ) ) ) ) ).
% insert_eq_iff
thf(fact_958_insert__absorb,axiom,
! [A2: set_state,A: set_set_state] :
( ( member_set_state @ A2 @ A )
=> ( ( insert_set_state @ A2 @ A )
= A ) ) ).
% insert_absorb
thf(fact_959_insert__absorb,axiom,
! [A2: set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ A2 @ A )
=> ( ( insert_set_set_state @ A2 @ A )
= A ) ) ).
% insert_absorb
thf(fact_960_insert__absorb,axiom,
! [A2: state,A: set_state] :
( ( member_state @ A2 @ A )
=> ( ( insert_state @ A2 @ A )
= A ) ) ).
% insert_absorb
thf(fact_961_insert__ident,axiom,
! [X2: set_state,A: set_set_state,B: set_set_state] :
( ~ ( member_set_state @ X2 @ A )
=> ( ~ ( member_set_state @ X2 @ B )
=> ( ( ( insert_set_state @ X2 @ A )
= ( insert_set_state @ X2 @ B ) )
= ( A = B ) ) ) ) ).
% insert_ident
thf(fact_962_insert__ident,axiom,
! [X2: set_set_state,A: set_set_set_state,B: set_set_set_state] :
( ~ ( member_set_set_state @ X2 @ A )
=> ( ~ ( member_set_set_state @ X2 @ B )
=> ( ( ( insert_set_set_state @ X2 @ A )
= ( insert_set_set_state @ X2 @ B ) )
= ( A = B ) ) ) ) ).
% insert_ident
thf(fact_963_insert__ident,axiom,
! [X2: state,A: set_state,B: set_state] :
( ~ ( member_state @ X2 @ A )
=> ( ~ ( member_state @ X2 @ B )
=> ( ( ( insert_state @ X2 @ A )
= ( insert_state @ X2 @ B ) )
= ( A = B ) ) ) ) ).
% insert_ident
thf(fact_964_Set_Oset__insert,axiom,
! [X2: set_state,A: set_set_state] :
( ( member_set_state @ X2 @ A )
=> ~ ! [B7: set_set_state] :
( ( A
= ( insert_set_state @ X2 @ B7 ) )
=> ( member_set_state @ X2 @ B7 ) ) ) ).
% Set.set_insert
thf(fact_965_Set_Oset__insert,axiom,
! [X2: set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ X2 @ A )
=> ~ ! [B7: set_set_set_state] :
( ( A
= ( insert_set_set_state @ X2 @ B7 ) )
=> ( member_set_set_state @ X2 @ B7 ) ) ) ).
% Set.set_insert
thf(fact_966_Set_Oset__insert,axiom,
! [X2: state,A: set_state] :
( ( member_state @ X2 @ A )
=> ~ ! [B7: set_state] :
( ( A
= ( insert_state @ X2 @ B7 ) )
=> ( member_state @ X2 @ B7 ) ) ) ).
% Set.set_insert
thf(fact_967_insertI2,axiom,
! [A2: set_state,B: set_set_state,B3: set_state] :
( ( member_set_state @ A2 @ B )
=> ( member_set_state @ A2 @ ( insert_set_state @ B3 @ B ) ) ) ).
% insertI2
thf(fact_968_insertI2,axiom,
! [A2: set_set_state,B: set_set_set_state,B3: set_set_state] :
( ( member_set_set_state @ A2 @ B )
=> ( member_set_set_state @ A2 @ ( insert_set_set_state @ B3 @ B ) ) ) ).
% insertI2
thf(fact_969_insertI2,axiom,
! [A2: state,B: set_state,B3: state] :
( ( member_state @ A2 @ B )
=> ( member_state @ A2 @ ( insert_state @ B3 @ B ) ) ) ).
% insertI2
thf(fact_970_insertI1,axiom,
! [A2: set_state,B: set_set_state] : ( member_set_state @ A2 @ ( insert_set_state @ A2 @ B ) ) ).
% insertI1
thf(fact_971_insertI1,axiom,
! [A2: set_set_state,B: set_set_set_state] : ( member_set_set_state @ A2 @ ( insert_set_set_state @ A2 @ B ) ) ).
% insertI1
thf(fact_972_insertI1,axiom,
! [A2: state,B: set_state] : ( member_state @ A2 @ ( insert_state @ A2 @ B ) ) ).
% insertI1
thf(fact_973_insertE,axiom,
! [A2: set_state,B3: set_state,A: set_set_state] :
( ( member_set_state @ A2 @ ( insert_set_state @ B3 @ A ) )
=> ( ( A2 != B3 )
=> ( member_set_state @ A2 @ A ) ) ) ).
% insertE
thf(fact_974_insertE,axiom,
! [A2: set_set_state,B3: set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ A2 @ ( insert_set_set_state @ B3 @ A ) )
=> ( ( A2 != B3 )
=> ( member_set_set_state @ A2 @ A ) ) ) ).
% insertE
thf(fact_975_insertE,axiom,
! [A2: state,B3: state,A: set_state] :
( ( member_state @ A2 @ ( insert_state @ B3 @ A ) )
=> ( ( A2 != B3 )
=> ( member_state @ A2 @ A ) ) ) ).
% insertE
thf(fact_976_bot__set__def,axiom,
( bot_bot_set_state
= ( collect_state @ bot_bot_state_o ) ) ).
% bot_set_def
thf(fact_977_bot__set__def,axiom,
( bot_bo2271482359692755898_state
= ( collect_set_state @ bot_bot_set_state_o ) ) ).
% bot_set_def
thf(fact_978_cInf__eq__minimum,axiom,
! [Z2: $o > set_state,X5: set_o_set_state] :
( ( member_o_set_state @ Z2 @ X5 )
=> ( ! [X: $o > set_state] :
( ( member_o_set_state @ X @ X5 )
=> ( ord_le9189382018855386905_state @ Z2 @ X ) )
=> ( ( comple1470863462450220288_state @ X5 )
= Z2 ) ) ) ).
% cInf_eq_minimum
thf(fact_979_cInf__eq__minimum,axiom,
! [Z2: set_set_state,X5: set_set_set_state] :
( ( member_set_set_state @ Z2 @ X5 )
=> ( ! [X: set_set_state] :
( ( member_set_set_state @ X @ X5 )
=> ( ord_le5175021213330142598_state @ Z2 @ X ) )
=> ( ( comple2682067033655477471_state @ X5 )
= Z2 ) ) ) ).
% cInf_eq_minimum
thf(fact_980_cInf__eq__minimum,axiom,
! [Z2: set_state,X5: set_set_state] :
( ( member_set_state @ Z2 @ X5 )
=> ( ! [X: set_state] :
( ( member_set_state @ X @ X5 )
=> ( ord_le2494988322063910608_state @ Z2 @ X ) )
=> ( ( comple1177038664686533161_state @ X5 )
= Z2 ) ) ) ).
% cInf_eq_minimum
thf(fact_981_insert__UNIV,axiom,
! [X2: state] :
( ( insert_state @ X2 @ top_top_set_state )
= top_top_set_state ) ).
% insert_UNIV
thf(fact_982_insert__UNIV,axiom,
! [X2: set_state] :
( ( insert_set_state @ X2 @ top_to5262587396890829782_state )
= top_to5262587396890829782_state ) ).
% insert_UNIV
thf(fact_983_singleton__inject,axiom,
! [A2: state,B3: state] :
( ( ( insert_state @ A2 @ bot_bot_set_state )
= ( insert_state @ B3 @ bot_bot_set_state ) )
=> ( A2 = B3 ) ) ).
% singleton_inject
thf(fact_984_singleton__inject,axiom,
! [A2: set_state,B3: set_state] :
( ( ( insert_set_state @ A2 @ bot_bo2271482359692755898_state )
= ( insert_set_state @ B3 @ bot_bo2271482359692755898_state ) )
=> ( A2 = B3 ) ) ).
% singleton_inject
thf(fact_985_insert__not__empty,axiom,
! [A2: state,A: set_state] :
( ( insert_state @ A2 @ A )
!= bot_bot_set_state ) ).
% insert_not_empty
thf(fact_986_insert__not__empty,axiom,
! [A2: set_state,A: set_set_state] :
( ( insert_set_state @ A2 @ A )
!= bot_bo2271482359692755898_state ) ).
% insert_not_empty
thf(fact_987_doubleton__eq__iff,axiom,
! [A2: state,B3: state,C: state,D: state] :
( ( ( insert_state @ A2 @ ( insert_state @ B3 @ bot_bot_set_state ) )
= ( insert_state @ C @ ( insert_state @ D @ bot_bot_set_state ) ) )
= ( ( ( A2 = C )
& ( B3 = D ) )
| ( ( A2 = D )
& ( B3 = C ) ) ) ) ).
% doubleton_eq_iff
thf(fact_988_doubleton__eq__iff,axiom,
! [A2: set_state,B3: set_state,C: set_state,D: set_state] :
( ( ( insert_set_state @ A2 @ ( insert_set_state @ B3 @ bot_bo2271482359692755898_state ) )
= ( insert_set_state @ C @ ( insert_set_state @ D @ bot_bo2271482359692755898_state ) ) )
= ( ( ( A2 = C )
& ( B3 = D ) )
| ( ( A2 = D )
& ( B3 = C ) ) ) ) ).
% doubleton_eq_iff
thf(fact_989_singleton__iff,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( member_set_set_state @ B3 @ ( insert_set_set_state @ A2 @ bot_bo7389043141884672880_state ) )
= ( B3 = A2 ) ) ).
% singleton_iff
thf(fact_990_singleton__iff,axiom,
! [B3: set_state,A2: set_state] :
( ( member_set_state @ B3 @ ( insert_set_state @ A2 @ bot_bo2271482359692755898_state ) )
= ( B3 = A2 ) ) ).
% singleton_iff
thf(fact_991_singleton__iff,axiom,
! [B3: state,A2: state] :
( ( member_state @ B3 @ ( insert_state @ A2 @ bot_bot_set_state ) )
= ( B3 = A2 ) ) ).
% singleton_iff
thf(fact_992_singletonD,axiom,
! [B3: set_set_state,A2: set_set_state] :
( ( member_set_set_state @ B3 @ ( insert_set_set_state @ A2 @ bot_bo7389043141884672880_state ) )
=> ( B3 = A2 ) ) ).
% singletonD
thf(fact_993_singletonD,axiom,
! [B3: set_state,A2: set_state] :
( ( member_set_state @ B3 @ ( insert_set_state @ A2 @ bot_bo2271482359692755898_state ) )
=> ( B3 = A2 ) ) ).
% singletonD
thf(fact_994_singletonD,axiom,
! [B3: state,A2: state] :
( ( member_state @ B3 @ ( insert_state @ A2 @ bot_bot_set_state ) )
=> ( B3 = A2 ) ) ).
% singletonD
thf(fact_995_subset__insertI2,axiom,
! [A: set_set_state,B: set_set_state,B3: set_state] :
( ( ord_le5175021213330142598_state @ A @ B )
=> ( ord_le5175021213330142598_state @ A @ ( insert_set_state @ B3 @ B ) ) ) ).
% subset_insertI2
thf(fact_996_subset__insertI2,axiom,
! [A: set_state,B: set_state,B3: state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ord_le2494988322063910608_state @ A @ ( insert_state @ B3 @ B ) ) ) ).
% subset_insertI2
thf(fact_997_subset__insertI,axiom,
! [B: set_set_state,A2: set_state] : ( ord_le5175021213330142598_state @ B @ ( insert_set_state @ A2 @ B ) ) ).
% subset_insertI
thf(fact_998_subset__insertI,axiom,
! [B: set_state,A2: state] : ( ord_le2494988322063910608_state @ B @ ( insert_state @ A2 @ B ) ) ).
% subset_insertI
thf(fact_999_subset__insert,axiom,
! [X2: set_set_state,A: set_set_set_state,B: set_set_set_state] :
( ~ ( member_set_set_state @ X2 @ A )
=> ( ( ord_le3154822624800881980_state @ A @ ( insert_set_set_state @ X2 @ B ) )
= ( ord_le3154822624800881980_state @ A @ B ) ) ) ).
% subset_insert
thf(fact_1000_subset__insert,axiom,
! [X2: set_state,A: set_set_state,B: set_set_state] :
( ~ ( member_set_state @ X2 @ A )
=> ( ( ord_le5175021213330142598_state @ A @ ( insert_set_state @ X2 @ B ) )
= ( ord_le5175021213330142598_state @ A @ B ) ) ) ).
% subset_insert
thf(fact_1001_subset__insert,axiom,
! [X2: state,A: set_state,B: set_state] :
( ~ ( member_state @ X2 @ A )
=> ( ( ord_le2494988322063910608_state @ A @ ( insert_state @ X2 @ B ) )
= ( ord_le2494988322063910608_state @ A @ B ) ) ) ).
% subset_insert
thf(fact_1002_insert__mono,axiom,
! [C2: set_set_state,D2: set_set_state,A2: set_state] :
( ( ord_le5175021213330142598_state @ C2 @ D2 )
=> ( ord_le5175021213330142598_state @ ( insert_set_state @ A2 @ C2 ) @ ( insert_set_state @ A2 @ D2 ) ) ) ).
% insert_mono
thf(fact_1003_insert__mono,axiom,
! [C2: set_state,D2: set_state,A2: state] :
( ( ord_le2494988322063910608_state @ C2 @ D2 )
=> ( ord_le2494988322063910608_state @ ( insert_state @ A2 @ C2 ) @ ( insert_state @ A2 @ D2 ) ) ) ).
% insert_mono
thf(fact_1004_pairwise__insert,axiom,
! [R3: set_state > set_state > $o,X2: set_state,S3: set_set_state] :
( ( pairwise_set_state @ R3 @ ( insert_set_state @ X2 @ S3 ) )
= ( ! [Y4: set_state] :
( ( ( member_set_state @ Y4 @ S3 )
& ( Y4 != X2 ) )
=> ( ( R3 @ X2 @ Y4 )
& ( R3 @ Y4 @ X2 ) ) )
& ( pairwise_set_state @ R3 @ S3 ) ) ) ).
% pairwise_insert
thf(fact_1005_pairwise__insert,axiom,
! [R3: set_set_state > set_set_state > $o,X2: set_set_state,S3: set_set_set_state] :
( ( pairwi6477347089298328827_state @ R3 @ ( insert_set_set_state @ X2 @ S3 ) )
= ( ! [Y4: set_set_state] :
( ( ( member_set_set_state @ Y4 @ S3 )
& ( Y4 != X2 ) )
=> ( ( R3 @ X2 @ Y4 )
& ( R3 @ Y4 @ X2 ) ) )
& ( pairwi6477347089298328827_state @ R3 @ S3 ) ) ) ).
% pairwise_insert
thf(fact_1006_pairwise__insert,axiom,
! [R3: state > state > $o,X2: state,S3: set_state] :
( ( pairwise_state @ R3 @ ( insert_state @ X2 @ S3 ) )
= ( ! [Y4: state] :
( ( ( member_state @ Y4 @ S3 )
& ( Y4 != X2 ) )
=> ( ( R3 @ X2 @ Y4 )
& ( R3 @ Y4 @ X2 ) ) )
& ( pairwise_state @ R3 @ S3 ) ) ) ).
% pairwise_insert
thf(fact_1007_cInf__eq__non__empty,axiom,
! [X5: set_o_set_state,A2: $o > set_state] :
( ( X5 != bot_bo782247444858010053_state )
=> ( ! [X: $o > set_state] :
( ( member_o_set_state @ X @ X5 )
=> ( ord_le9189382018855386905_state @ A2 @ X ) )
=> ( ! [Y2: $o > set_state] :
( ! [X6: $o > set_state] :
( ( member_o_set_state @ X6 @ X5 )
=> ( ord_le9189382018855386905_state @ Y2 @ X6 ) )
=> ( ord_le9189382018855386905_state @ Y2 @ A2 ) )
=> ( ( comple1470863462450220288_state @ X5 )
= A2 ) ) ) ) ).
% cInf_eq_non_empty
thf(fact_1008_cInf__eq__non__empty,axiom,
! [X5: set_set_set_state,A2: set_set_state] :
( ( X5 != bot_bo7389043141884672880_state )
=> ( ! [X: set_set_state] :
( ( member_set_set_state @ X @ X5 )
=> ( ord_le5175021213330142598_state @ A2 @ X ) )
=> ( ! [Y2: set_set_state] :
( ! [X6: set_set_state] :
( ( member_set_set_state @ X6 @ X5 )
=> ( ord_le5175021213330142598_state @ Y2 @ X6 ) )
=> ( ord_le5175021213330142598_state @ Y2 @ A2 ) )
=> ( ( comple2682067033655477471_state @ X5 )
= A2 ) ) ) ) ).
% cInf_eq_non_empty
thf(fact_1009_cInf__eq__non__empty,axiom,
! [X5: set_set_state,A2: set_state] :
( ( X5 != bot_bo2271482359692755898_state )
=> ( ! [X: set_state] :
( ( member_set_state @ X @ X5 )
=> ( ord_le2494988322063910608_state @ A2 @ X ) )
=> ( ! [Y2: set_state] :
( ! [X6: set_state] :
( ( member_set_state @ X6 @ X5 )
=> ( ord_le2494988322063910608_state @ Y2 @ X6 ) )
=> ( ord_le2494988322063910608_state @ Y2 @ A2 ) )
=> ( ( comple1177038664686533161_state @ X5 )
= A2 ) ) ) ) ).
% cInf_eq_non_empty
thf(fact_1010_cInf__greatest,axiom,
! [X5: set_o_set_state,Z2: $o > set_state] :
( ( X5 != bot_bo782247444858010053_state )
=> ( ! [X: $o > set_state] :
( ( member_o_set_state @ X @ X5 )
=> ( ord_le9189382018855386905_state @ Z2 @ X ) )
=> ( ord_le9189382018855386905_state @ Z2 @ ( comple1470863462450220288_state @ X5 ) ) ) ) ).
% cInf_greatest
thf(fact_1011_cInf__greatest,axiom,
! [X5: set_set_set_state,Z2: set_set_state] :
( ( X5 != bot_bo7389043141884672880_state )
=> ( ! [X: set_set_state] :
( ( member_set_set_state @ X @ X5 )
=> ( ord_le5175021213330142598_state @ Z2 @ X ) )
=> ( ord_le5175021213330142598_state @ Z2 @ ( comple2682067033655477471_state @ X5 ) ) ) ) ).
% cInf_greatest
thf(fact_1012_cInf__greatest,axiom,
! [X5: set_set_state,Z2: set_state] :
( ( X5 != bot_bo2271482359692755898_state )
=> ( ! [X: set_state] :
( ( member_set_state @ X @ X5 )
=> ( ord_le2494988322063910608_state @ Z2 @ X ) )
=> ( ord_le2494988322063910608_state @ Z2 @ ( comple1177038664686533161_state @ X5 ) ) ) ) ).
% cInf_greatest
thf(fact_1013_subset__singleton__iff,axiom,
! [X5: set_set_state,A2: set_state] :
( ( ord_le5175021213330142598_state @ X5 @ ( insert_set_state @ A2 @ bot_bo2271482359692755898_state ) )
= ( ( X5 = bot_bo2271482359692755898_state )
| ( X5
= ( insert_set_state @ A2 @ bot_bo2271482359692755898_state ) ) ) ) ).
% subset_singleton_iff
thf(fact_1014_subset__singleton__iff,axiom,
! [X5: set_state,A2: state] :
( ( ord_le2494988322063910608_state @ X5 @ ( insert_state @ A2 @ bot_bot_set_state ) )
= ( ( X5 = bot_bot_set_state )
| ( X5
= ( insert_state @ A2 @ bot_bot_set_state ) ) ) ) ).
% subset_singleton_iff
thf(fact_1015_subset__singletonD,axiom,
! [A: set_set_state,X2: set_state] :
( ( ord_le5175021213330142598_state @ A @ ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) )
=> ( ( A = bot_bo2271482359692755898_state )
| ( A
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) ) ) ) ).
% subset_singletonD
thf(fact_1016_subset__singletonD,axiom,
! [A: set_state,X2: state] :
( ( ord_le2494988322063910608_state @ A @ ( insert_state @ X2 @ bot_bot_set_state ) )
=> ( ( A = bot_bot_set_state )
| ( A
= ( insert_state @ X2 @ bot_bot_set_state ) ) ) ) ).
% subset_singletonD
thf(fact_1017_singleton__Un__iff,axiom,
! [X2: state,A: set_state,B: set_state] :
( ( ( insert_state @ X2 @ bot_bot_set_state )
= ( sup_sup_set_state @ A @ B ) )
= ( ( ( A = bot_bot_set_state )
& ( B
= ( insert_state @ X2 @ bot_bot_set_state ) ) )
| ( ( A
= ( insert_state @ X2 @ bot_bot_set_state ) )
& ( B = bot_bot_set_state ) )
| ( ( A
= ( insert_state @ X2 @ bot_bot_set_state ) )
& ( B
= ( insert_state @ X2 @ bot_bot_set_state ) ) ) ) ) ).
% singleton_Un_iff
thf(fact_1018_singleton__Un__iff,axiom,
! [X2: set_state,A: set_set_state,B: set_set_state] :
( ( ( insert_set_state @ X2 @ bot_bo2271482359692755898_state )
= ( sup_su4188871578264421970_state @ A @ B ) )
= ( ( ( A = bot_bo2271482359692755898_state )
& ( B
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) ) )
| ( ( A
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) )
& ( B = bot_bo2271482359692755898_state ) )
| ( ( A
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) )
& ( B
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) ) ) ) ) ).
% singleton_Un_iff
thf(fact_1019_Un__singleton__iff,axiom,
! [A: set_state,B: set_state,X2: state] :
( ( ( sup_sup_set_state @ A @ B )
= ( insert_state @ X2 @ bot_bot_set_state ) )
= ( ( ( A = bot_bot_set_state )
& ( B
= ( insert_state @ X2 @ bot_bot_set_state ) ) )
| ( ( A
= ( insert_state @ X2 @ bot_bot_set_state ) )
& ( B = bot_bot_set_state ) )
| ( ( A
= ( insert_state @ X2 @ bot_bot_set_state ) )
& ( B
= ( insert_state @ X2 @ bot_bot_set_state ) ) ) ) ) ).
% Un_singleton_iff
thf(fact_1020_Un__singleton__iff,axiom,
! [A: set_set_state,B: set_set_state,X2: set_state] :
( ( ( sup_su4188871578264421970_state @ A @ B )
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) )
= ( ( ( A = bot_bo2271482359692755898_state )
& ( B
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) ) )
| ( ( A
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) )
& ( B = bot_bo2271482359692755898_state ) )
| ( ( A
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) )
& ( B
= ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) ) ) ) ) ).
% Un_singleton_iff
thf(fact_1021_insert__is__Un,axiom,
( insert_state
= ( ^ [A4: state] : ( sup_sup_set_state @ ( insert_state @ A4 @ bot_bot_set_state ) ) ) ) ).
% insert_is_Un
thf(fact_1022_insert__is__Un,axiom,
( insert_set_state
= ( ^ [A4: set_state] : ( sup_su4188871578264421970_state @ ( insert_set_state @ A4 @ bot_bo2271482359692755898_state ) ) ) ) ).
% insert_is_Un
thf(fact_1023_atLeastAtMost__singleton_H,axiom,
! [A2: set_state,B3: set_state] :
( ( A2 = B3 )
=> ( ( set_or701696889746204795_state @ A2 @ B3 )
= ( insert_set_state @ A2 @ bot_bo2271482359692755898_state ) ) ) ).
% atLeastAtMost_singleton'
thf(fact_1024_pairwise__singleton,axiom,
! [P: state > state > $o,A: state] : ( pairwise_state @ P @ ( insert_state @ A @ bot_bot_set_state ) ) ).
% pairwise_singleton
thf(fact_1025_pairwise__singleton,axiom,
! [P: set_state > set_state > $o,A: set_state] : ( pairwise_set_state @ P @ ( insert_set_state @ A @ bot_bo2271482359692755898_state ) ) ).
% pairwise_singleton
thf(fact_1026_Inf__empty,axiom,
( ( comple6810834910230287260tate_o @ bot_bot_set_state_o2 )
= top_top_state_o ) ).
% Inf_empty
thf(fact_1027_Inf__empty,axiom,
( ( comple2682067033655477471_state @ bot_bo7389043141884672880_state )
= top_to5262587396890829782_state ) ).
% Inf_empty
thf(fact_1028_Inf__empty,axiom,
( ( comple1177038664686533161_state @ bot_bo2271482359692755898_state )
= top_top_set_state ) ).
% Inf_empty
thf(fact_1029_Inf__UNIV,axiom,
( ( comple2682067033655477471_state @ top_to3598970937283095436_state )
= bot_bo2271482359692755898_state ) ).
% Inf_UNIV
thf(fact_1030_Inf__UNIV,axiom,
( ( comple1177038664686533161_state @ top_to5262587396890829782_state )
= bot_bot_set_state ) ).
% Inf_UNIV
thf(fact_1031_Inf__top__conv_I2_J,axiom,
! [A: set_state_o] :
( ( top_top_state_o
= ( comple6810834910230287260tate_o @ A ) )
= ( ! [X3: state > $o] :
( ( member_state_o @ X3 @ A )
=> ( X3 = top_top_state_o ) ) ) ) ).
% Inf_top_conv(2)
thf(fact_1032_Inf__top__conv_I2_J,axiom,
! [A: set_set_set_state] :
( ( top_to5262587396890829782_state
= ( comple2682067033655477471_state @ A ) )
= ( ! [X3: set_set_state] :
( ( member_set_set_state @ X3 @ A )
=> ( X3 = top_to5262587396890829782_state ) ) ) ) ).
% Inf_top_conv(2)
thf(fact_1033_Inf__top__conv_I2_J,axiom,
! [A: set_set_state] :
( ( top_top_set_state
= ( comple1177038664686533161_state @ A ) )
= ( ! [X3: set_state] :
( ( member_set_state @ X3 @ A )
=> ( X3 = top_top_set_state ) ) ) ) ).
% Inf_top_conv(2)
thf(fact_1034_Inter__UNIV__conv_I1_J,axiom,
! [A: set_set_set_state] :
( ( ( comple2682067033655477471_state @ A )
= top_to5262587396890829782_state )
= ( ! [X3: set_set_state] :
( ( member_set_set_state @ X3 @ A )
=> ( X3 = top_to5262587396890829782_state ) ) ) ) ).
% Inter_UNIV_conv(1)
thf(fact_1035_Inter__UNIV__conv_I1_J,axiom,
! [A: set_set_state] :
( ( ( comple1177038664686533161_state @ A )
= top_top_set_state )
= ( ! [X3: set_state] :
( ( member_set_state @ X3 @ A )
=> ( X3 = top_top_set_state ) ) ) ) ).
% Inter_UNIV_conv(1)
thf(fact_1036_Inter__UNIV__conv_I2_J,axiom,
! [A: set_set_set_state] :
( ( top_to5262587396890829782_state
= ( comple2682067033655477471_state @ A ) )
= ( ! [X3: set_set_state] :
( ( member_set_set_state @ X3 @ A )
=> ( X3 = top_to5262587396890829782_state ) ) ) ) ).
% Inter_UNIV_conv(2)
thf(fact_1037_Inter__UNIV__conv_I2_J,axiom,
! [A: set_set_state] :
( ( top_top_set_state
= ( comple1177038664686533161_state @ A ) )
= ( ! [X3: set_state] :
( ( member_set_state @ X3 @ A )
=> ( X3 = top_top_set_state ) ) ) ) ).
% Inter_UNIV_conv(2)
thf(fact_1038_Inf__top__conv_I1_J,axiom,
! [A: set_state_o] :
( ( ( comple6810834910230287260tate_o @ A )
= top_top_state_o )
= ( ! [X3: state > $o] :
( ( member_state_o @ X3 @ A )
=> ( X3 = top_top_state_o ) ) ) ) ).
% Inf_top_conv(1)
thf(fact_1039_Inf__top__conv_I1_J,axiom,
! [A: set_set_set_state] :
( ( ( comple2682067033655477471_state @ A )
= top_to5262587396890829782_state )
= ( ! [X3: set_set_state] :
( ( member_set_set_state @ X3 @ A )
=> ( X3 = top_to5262587396890829782_state ) ) ) ) ).
% Inf_top_conv(1)
thf(fact_1040_Inf__top__conv_I1_J,axiom,
! [A: set_set_state] :
( ( ( comple1177038664686533161_state @ A )
= top_top_set_state )
= ( ! [X3: set_state] :
( ( member_set_state @ X3 @ A )
=> ( X3 = top_top_set_state ) ) ) ) ).
% Inf_top_conv(1)
thf(fact_1041_Inter__empty,axiom,
( ( comple2682067033655477471_state @ bot_bo7389043141884672880_state )
= top_to5262587396890829782_state ) ).
% Inter_empty
thf(fact_1042_Inter__empty,axiom,
( ( comple1177038664686533161_state @ bot_bo2271482359692755898_state )
= top_top_set_state ) ).
% Inter_empty
thf(fact_1043_Inter__anti__mono,axiom,
! [B: set_set_set_state,A: set_set_set_state] :
( ( ord_le3154822624800881980_state @ B @ A )
=> ( ord_le5175021213330142598_state @ ( comple2682067033655477471_state @ A ) @ ( comple2682067033655477471_state @ B ) ) ) ).
% Inter_anti_mono
thf(fact_1044_Inter__anti__mono,axiom,
! [B: set_set_state,A: set_set_state] :
( ( ord_le5175021213330142598_state @ B @ A )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ A ) @ ( comple1177038664686533161_state @ B ) ) ) ).
% Inter_anti_mono
thf(fact_1045_Inter__greatest,axiom,
! [A: set_set_set_state,C2: set_set_state] :
( ! [X7: set_set_state] :
( ( member_set_set_state @ X7 @ A )
=> ( ord_le5175021213330142598_state @ C2 @ X7 ) )
=> ( ord_le5175021213330142598_state @ C2 @ ( comple2682067033655477471_state @ A ) ) ) ).
% Inter_greatest
thf(fact_1046_Inter__greatest,axiom,
! [A: set_set_state,C2: set_state] :
( ! [X7: set_state] :
( ( member_set_state @ X7 @ A )
=> ( ord_le2494988322063910608_state @ C2 @ X7 ) )
=> ( ord_le2494988322063910608_state @ C2 @ ( comple1177038664686533161_state @ A ) ) ) ).
% Inter_greatest
thf(fact_1047_Inter__lower,axiom,
! [B: set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ B @ A )
=> ( ord_le5175021213330142598_state @ ( comple2682067033655477471_state @ A ) @ B ) ) ).
% Inter_lower
thf(fact_1048_Inter__lower,axiom,
! [B: set_state,A: set_set_state] :
( ( member_set_state @ B @ A )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ A ) @ B ) ) ).
% Inter_lower
thf(fact_1049_Inter__subset,axiom,
! [A: set_set_set_state,B: set_set_state] :
( ! [X7: set_set_state] :
( ( member_set_set_state @ X7 @ A )
=> ( ord_le5175021213330142598_state @ X7 @ B ) )
=> ( ( A != bot_bo7389043141884672880_state )
=> ( ord_le5175021213330142598_state @ ( comple2682067033655477471_state @ A ) @ B ) ) ) ).
% Inter_subset
thf(fact_1050_Inter__subset,axiom,
! [A: set_set_state,B: set_state] :
( ! [X7: set_state] :
( ( member_set_state @ X7 @ A )
=> ( ord_le2494988322063910608_state @ X7 @ B ) )
=> ( ( A != bot_bo2271482359692755898_state )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ A ) @ B ) ) ) ).
% Inter_subset
thf(fact_1051_Inf__greatest,axiom,
! [A: set_o_set_state,Z2: $o > set_state] :
( ! [X: $o > set_state] :
( ( member_o_set_state @ X @ A )
=> ( ord_le9189382018855386905_state @ Z2 @ X ) )
=> ( ord_le9189382018855386905_state @ Z2 @ ( comple1470863462450220288_state @ A ) ) ) ).
% Inf_greatest
thf(fact_1052_Inf__greatest,axiom,
! [A: set_set_set_state,Z2: set_set_state] :
( ! [X: set_set_state] :
( ( member_set_set_state @ X @ A )
=> ( ord_le5175021213330142598_state @ Z2 @ X ) )
=> ( ord_le5175021213330142598_state @ Z2 @ ( comple2682067033655477471_state @ A ) ) ) ).
% Inf_greatest
thf(fact_1053_Inf__greatest,axiom,
! [A: set_set_state,Z2: set_state] :
( ! [X: set_state] :
( ( member_set_state @ X @ A )
=> ( ord_le2494988322063910608_state @ Z2 @ X ) )
=> ( ord_le2494988322063910608_state @ Z2 @ ( comple1177038664686533161_state @ A ) ) ) ).
% Inf_greatest
thf(fact_1054_le__Inf__iff,axiom,
! [B3: $o > set_state,A: set_o_set_state] :
( ( ord_le9189382018855386905_state @ B3 @ ( comple1470863462450220288_state @ A ) )
= ( ! [X3: $o > set_state] :
( ( member_o_set_state @ X3 @ A )
=> ( ord_le9189382018855386905_state @ B3 @ X3 ) ) ) ) ).
% le_Inf_iff
thf(fact_1055_le__Inf__iff,axiom,
! [B3: set_set_state,A: set_set_set_state] :
( ( ord_le5175021213330142598_state @ B3 @ ( comple2682067033655477471_state @ A ) )
= ( ! [X3: set_set_state] :
( ( member_set_set_state @ X3 @ A )
=> ( ord_le5175021213330142598_state @ B3 @ X3 ) ) ) ) ).
% le_Inf_iff
thf(fact_1056_le__Inf__iff,axiom,
! [B3: set_state,A: set_set_state] :
( ( ord_le2494988322063910608_state @ B3 @ ( comple1177038664686533161_state @ A ) )
= ( ! [X3: set_state] :
( ( member_set_state @ X3 @ A )
=> ( ord_le2494988322063910608_state @ B3 @ X3 ) ) ) ) ).
% le_Inf_iff
thf(fact_1057_Inf__lower2,axiom,
! [U: $o > set_state,A: set_o_set_state,V: $o > set_state] :
( ( member_o_set_state @ U @ A )
=> ( ( ord_le9189382018855386905_state @ U @ V )
=> ( ord_le9189382018855386905_state @ ( comple1470863462450220288_state @ A ) @ V ) ) ) ).
% Inf_lower2
thf(fact_1058_Inf__lower2,axiom,
! [U: set_set_state,A: set_set_set_state,V: set_set_state] :
( ( member_set_set_state @ U @ A )
=> ( ( ord_le5175021213330142598_state @ U @ V )
=> ( ord_le5175021213330142598_state @ ( comple2682067033655477471_state @ A ) @ V ) ) ) ).
% Inf_lower2
thf(fact_1059_Inf__lower2,axiom,
! [U: set_state,A: set_set_state,V: set_state] :
( ( member_set_state @ U @ A )
=> ( ( ord_le2494988322063910608_state @ U @ V )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ A ) @ V ) ) ) ).
% Inf_lower2
thf(fact_1060_Inf__lower,axiom,
! [X2: $o > set_state,A: set_o_set_state] :
( ( member_o_set_state @ X2 @ A )
=> ( ord_le9189382018855386905_state @ ( comple1470863462450220288_state @ A ) @ X2 ) ) ).
% Inf_lower
thf(fact_1061_Inf__lower,axiom,
! [X2: set_set_state,A: set_set_set_state] :
( ( member_set_set_state @ X2 @ A )
=> ( ord_le5175021213330142598_state @ ( comple2682067033655477471_state @ A ) @ X2 ) ) ).
% Inf_lower
thf(fact_1062_Inf__lower,axiom,
! [X2: set_state,A: set_set_state] :
( ( member_set_state @ X2 @ A )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ A ) @ X2 ) ) ).
% Inf_lower
thf(fact_1063_Inf__mono,axiom,
! [B: set_o_set_state,A: set_o_set_state] :
( ! [B5: $o > set_state] :
( ( member_o_set_state @ B5 @ B )
=> ? [X6: $o > set_state] :
( ( member_o_set_state @ X6 @ A )
& ( ord_le9189382018855386905_state @ X6 @ B5 ) ) )
=> ( ord_le9189382018855386905_state @ ( comple1470863462450220288_state @ A ) @ ( comple1470863462450220288_state @ B ) ) ) ).
% Inf_mono
thf(fact_1064_Inf__mono,axiom,
! [B: set_set_set_state,A: set_set_set_state] :
( ! [B5: set_set_state] :
( ( member_set_set_state @ B5 @ B )
=> ? [X6: set_set_state] :
( ( member_set_set_state @ X6 @ A )
& ( ord_le5175021213330142598_state @ X6 @ B5 ) ) )
=> ( ord_le5175021213330142598_state @ ( comple2682067033655477471_state @ A ) @ ( comple2682067033655477471_state @ B ) ) ) ).
% Inf_mono
thf(fact_1065_Inf__mono,axiom,
! [B: set_set_state,A: set_set_state] :
( ! [B5: set_state] :
( ( member_set_state @ B5 @ B )
=> ? [X6: set_state] :
( ( member_set_state @ X6 @ A )
& ( ord_le2494988322063910608_state @ X6 @ B5 ) ) )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ A ) @ ( comple1177038664686533161_state @ B ) ) ) ).
% Inf_mono
thf(fact_1066_Inf__eqI,axiom,
! [A: set_o_set_state,X2: $o > set_state] :
( ! [I2: $o > set_state] :
( ( member_o_set_state @ I2 @ A )
=> ( ord_le9189382018855386905_state @ X2 @ I2 ) )
=> ( ! [Y2: $o > set_state] :
( ! [I3: $o > set_state] :
( ( member_o_set_state @ I3 @ A )
=> ( ord_le9189382018855386905_state @ Y2 @ I3 ) )
=> ( ord_le9189382018855386905_state @ Y2 @ X2 ) )
=> ( ( comple1470863462450220288_state @ A )
= X2 ) ) ) ).
% Inf_eqI
thf(fact_1067_Inf__eqI,axiom,
! [A: set_set_set_state,X2: set_set_state] :
( ! [I2: set_set_state] :
( ( member_set_set_state @ I2 @ A )
=> ( ord_le5175021213330142598_state @ X2 @ I2 ) )
=> ( ! [Y2: set_set_state] :
( ! [I3: set_set_state] :
( ( member_set_set_state @ I3 @ A )
=> ( ord_le5175021213330142598_state @ Y2 @ I3 ) )
=> ( ord_le5175021213330142598_state @ Y2 @ X2 ) )
=> ( ( comple2682067033655477471_state @ A )
= X2 ) ) ) ).
% Inf_eqI
thf(fact_1068_Inf__eqI,axiom,
! [A: set_set_state,X2: set_state] :
( ! [I2: set_state] :
( ( member_set_state @ I2 @ A )
=> ( ord_le2494988322063910608_state @ X2 @ I2 ) )
=> ( ! [Y2: set_state] :
( ! [I3: set_state] :
( ( member_set_state @ I3 @ A )
=> ( ord_le2494988322063910608_state @ Y2 @ I3 ) )
=> ( ord_le2494988322063910608_state @ Y2 @ X2 ) )
=> ( ( comple1177038664686533161_state @ A )
= X2 ) ) ) ).
% Inf_eqI
thf(fact_1069_Inter__UNIV,axiom,
( ( comple2682067033655477471_state @ top_to3598970937283095436_state )
= bot_bo2271482359692755898_state ) ).
% Inter_UNIV
thf(fact_1070_Inter__UNIV,axiom,
( ( comple1177038664686533161_state @ top_to5262587396890829782_state )
= bot_bot_set_state ) ).
% Inter_UNIV
thf(fact_1071_Inf__less__eq,axiom,
! [A: set_o_set_state,U: $o > set_state] :
( ! [V2: $o > set_state] :
( ( member_o_set_state @ V2 @ A )
=> ( ord_le9189382018855386905_state @ V2 @ U ) )
=> ( ( A != bot_bo782247444858010053_state )
=> ( ord_le9189382018855386905_state @ ( comple1470863462450220288_state @ A ) @ U ) ) ) ).
% Inf_less_eq
thf(fact_1072_Inf__less__eq,axiom,
! [A: set_set_set_state,U: set_set_state] :
( ! [V2: set_set_state] :
( ( member_set_set_state @ V2 @ A )
=> ( ord_le5175021213330142598_state @ V2 @ U ) )
=> ( ( A != bot_bo7389043141884672880_state )
=> ( ord_le5175021213330142598_state @ ( comple2682067033655477471_state @ A ) @ U ) ) ) ).
% Inf_less_eq
thf(fact_1073_Inf__less__eq,axiom,
! [A: set_set_state,U: set_state] :
( ! [V2: set_state] :
( ( member_set_state @ V2 @ A )
=> ( ord_le2494988322063910608_state @ V2 @ U ) )
=> ( ( A != bot_bo2271482359692755898_state )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ A ) @ U ) ) ) ).
% Inf_less_eq
thf(fact_1074_Inf__superset__mono,axiom,
! [B: set_o_set_state,A: set_o_set_state] :
( ( ord_le4652835513209282297_state @ B @ A )
=> ( ord_le9189382018855386905_state @ ( comple1470863462450220288_state @ A ) @ ( comple1470863462450220288_state @ B ) ) ) ).
% Inf_superset_mono
thf(fact_1075_Inf__superset__mono,axiom,
! [B: set_set_set_state,A: set_set_set_state] :
( ( ord_le3154822624800881980_state @ B @ A )
=> ( ord_le5175021213330142598_state @ ( comple2682067033655477471_state @ A ) @ ( comple2682067033655477471_state @ B ) ) ) ).
% Inf_superset_mono
thf(fact_1076_Inf__superset__mono,axiom,
! [B: set_set_state,A: set_set_state] :
( ( ord_le5175021213330142598_state @ B @ A )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ A ) @ ( comple1177038664686533161_state @ B ) ) ) ).
% Inf_superset_mono
thf(fact_1077_Inf__sup__eq__top__iff,axiom,
! [B: set_state_state_o,A2: state > state > $o] :
( ( ( sup_su7525921995284788454tate_o @ ( comple3128546889576232729tate_o @ B ) @ A2 )
= top_to5868225466921797218tate_o )
= ( ! [X3: state > state > $o] :
( ( member_state_state_o @ X3 @ B )
=> ( ( sup_su7525921995284788454tate_o @ X3 @ A2 )
= top_to5868225466921797218tate_o ) ) ) ) ).
% Inf_sup_eq_top_iff
thf(fact_1078_Inf__sup__eq__top__iff,axiom,
! [B: set_state_o,A2: state > $o] :
( ( ( sup_sup_state_o @ ( comple6810834910230287260tate_o @ B ) @ A2 )
= top_top_state_o )
= ( ! [X3: state > $o] :
( ( member_state_o @ X3 @ B )
=> ( ( sup_sup_state_o @ X3 @ A2 )
= top_top_state_o ) ) ) ) ).
% Inf_sup_eq_top_iff
thf(fact_1079_Inf__sup__eq__top__iff,axiom,
! [B: set_set_set_state,A2: set_set_state] :
( ( ( sup_su4188871578264421970_state @ ( comple2682067033655477471_state @ B ) @ A2 )
= top_to5262587396890829782_state )
= ( ! [X3: set_set_state] :
( ( member_set_set_state @ X3 @ B )
=> ( ( sup_su4188871578264421970_state @ X3 @ A2 )
= top_to5262587396890829782_state ) ) ) ) ).
% Inf_sup_eq_top_iff
thf(fact_1080_Inf__sup__eq__top__iff,axiom,
! [B: set_set_state,A2: set_state] :
( ( ( sup_sup_set_state @ ( comple1177038664686533161_state @ B ) @ A2 )
= top_top_set_state )
= ( ! [X3: set_state] :
( ( member_set_state @ X3 @ B )
=> ( ( sup_sup_set_state @ X3 @ A2 )
= top_top_set_state ) ) ) ) ).
% Inf_sup_eq_top_iff
thf(fact_1081_the__elem__eq,axiom,
! [X2: state] :
( ( the_elem_state @ ( insert_state @ X2 @ bot_bot_set_state ) )
= X2 ) ).
% the_elem_eq
thf(fact_1082_the__elem__eq,axiom,
! [X2: set_state] :
( ( the_elem_set_state @ ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) )
= X2 ) ).
% the_elem_eq
thf(fact_1083_is__singletonI,axiom,
! [X2: state] : ( is_singleton_state @ ( insert_state @ X2 @ bot_bot_set_state ) ) ).
% is_singletonI
thf(fact_1084_is__singletonI,axiom,
! [X2: set_state] : ( is_sin3747817797122030204_state @ ( insert_set_state @ X2 @ bot_bo2271482359692755898_state ) ) ).
% is_singletonI
thf(fact_1085_is__singleton__the__elem,axiom,
( is_singleton_state
= ( ^ [A3: set_state] :
( A3
= ( insert_state @ ( the_elem_state @ A3 ) @ bot_bot_set_state ) ) ) ) ).
% is_singleton_the_elem
thf(fact_1086_is__singleton__the__elem,axiom,
( is_sin3747817797122030204_state
= ( ^ [A3: set_set_state] :
( A3
= ( insert_set_state @ ( the_elem_set_state @ A3 ) @ bot_bo2271482359692755898_state ) ) ) ) ).
% is_singleton_the_elem
thf(fact_1087_is__singletonI_H,axiom,
! [A: set_set_set_state] :
( ( A != bot_bo7389043141884672880_state )
=> ( ! [X: set_set_state,Y2: set_set_state] :
( ( member_set_set_state @ X @ A )
=> ( ( member_set_set_state @ Y2 @ A )
=> ( X = Y2 ) ) )
=> ( is_sin6783755808700971314_state @ A ) ) ) ).
% is_singletonI'
thf(fact_1088_is__singletonI_H,axiom,
! [A: set_set_state] :
( ( A != bot_bo2271482359692755898_state )
=> ( ! [X: set_state,Y2: set_state] :
( ( member_set_state @ X @ A )
=> ( ( member_set_state @ Y2 @ A )
=> ( X = Y2 ) ) )
=> ( is_sin3747817797122030204_state @ A ) ) ) ).
% is_singletonI'
thf(fact_1089_is__singletonI_H,axiom,
! [A: set_state] :
( ( A != bot_bot_set_state )
=> ( ! [X: state,Y2: state] :
( ( member_state @ X @ A )
=> ( ( member_state @ Y2 @ A )
=> ( X = Y2 ) ) )
=> ( is_singleton_state @ A ) ) ) ).
% is_singletonI'
thf(fact_1090_is__singletonE,axiom,
! [A: set_state] :
( ( is_singleton_state @ A )
=> ~ ! [X: state] :
( A
!= ( insert_state @ X @ bot_bot_set_state ) ) ) ).
% is_singletonE
thf(fact_1091_is__singletonE,axiom,
! [A: set_set_state] :
( ( is_sin3747817797122030204_state @ A )
=> ~ ! [X: set_state] :
( A
!= ( insert_set_state @ X @ bot_bo2271482359692755898_state ) ) ) ).
% is_singletonE
thf(fact_1092_is__singleton__def,axiom,
( is_singleton_state
= ( ^ [A3: set_state] :
? [X3: state] :
( A3
= ( insert_state @ X3 @ bot_bot_set_state ) ) ) ) ).
% is_singleton_def
thf(fact_1093_is__singleton__def,axiom,
( is_sin3747817797122030204_state
= ( ^ [A3: set_set_state] :
? [X3: set_state] :
( A3
= ( insert_set_state @ X3 @ bot_bo2271482359692755898_state ) ) ) ) ).
% is_singleton_def
thf(fact_1094_atMost__Int__atLeast,axiom,
! [N: set_state] :
( ( inf_in8939913482472430008_state @ ( set_or5536065684288934121_state @ N ) @ ( set_or6477372120337742821_state @ N ) )
= ( insert_set_state @ N @ bot_bo2271482359692755898_state ) ) ).
% atMost_Int_atLeast
thf(fact_1095_greaterThanAtMost__eq__atLeastAtMost__diff,axiom,
( set_or5184245929044373792_state
= ( ^ [A4: set_state,B4: set_state] : ( minus_5895981879909142783_state @ ( set_or701696889746204795_state @ A4 @ B4 ) @ ( insert_set_state @ A4 @ bot_bo2271482359692755898_state ) ) ) ) ).
% greaterThanAtMost_eq_atLeastAtMost_diff
thf(fact_1096_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
( set_or2838015025653527455_state
= ( ^ [A4: set_state,B4: set_state] : ( minus_5895981879909142783_state @ ( set_or701696889746204795_state @ A4 @ B4 ) @ ( insert_set_state @ B4 @ bot_bo2271482359692755898_state ) ) ) ) ).
% atLeastLessThan_eq_atLeastAtMost_diff
thf(fact_1097_inf_Oidem,axiom,
! [A2: set_state] :
( ( inf_inf_set_state @ A2 @ A2 )
= A2 ) ).
% inf.idem
thf(fact_1098_inf_Oidem,axiom,
! [A2: set_set_state] :
( ( inf_in8939913482472430008_state @ A2 @ A2 )
= A2 ) ).
% inf.idem
thf(fact_1099_inf__idem,axiom,
! [X2: set_state] :
( ( inf_inf_set_state @ X2 @ X2 )
= X2 ) ).
% inf_idem
thf(fact_1100_inf__idem,axiom,
! [X2: set_set_state] :
( ( inf_in8939913482472430008_state @ X2 @ X2 )
= X2 ) ).
% inf_idem
thf(fact_1101_inf_Oleft__idem,axiom,
! [A2: set_state,B3: set_state] :
( ( inf_inf_set_state @ A2 @ ( inf_inf_set_state @ A2 @ B3 ) )
= ( inf_inf_set_state @ A2 @ B3 ) ) ).
% inf.left_idem
thf(fact_1102_inf_Oleft__idem,axiom,
! [A2: set_set_state,B3: set_set_state] :
( ( inf_in8939913482472430008_state @ A2 @ ( inf_in8939913482472430008_state @ A2 @ B3 ) )
= ( inf_in8939913482472430008_state @ A2 @ B3 ) ) ).
% inf.left_idem
thf(fact_1103_IntI,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ A )
=> ( ( member_state @ C @ B )
=> ( member_state @ C @ ( inf_inf_set_state @ A @ B ) ) ) ) ).
% IntI
thf(fact_1104_Int__iff,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( inf_inf_set_state @ A @ B ) )
= ( ( member_state @ C @ A )
& ( member_state @ C @ B ) ) ) ).
% Int_iff
thf(fact_1105_DiffI,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ A )
=> ( ~ ( member_state @ C @ B )
=> ( member_state @ C @ ( minus_3933957440811877961_state @ A @ B ) ) ) ) ).
% DiffI
thf(fact_1106_Diff__iff,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( minus_3933957440811877961_state @ A @ B ) )
= ( ( member_state @ C @ A )
& ~ ( member_state @ C @ B ) ) ) ).
% Diff_iff
thf(fact_1107_le__inf__iff,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ ( inf_inf_set_state @ Y @ Z2 ) )
= ( ( ord_le2494988322063910608_state @ X2 @ Y )
& ( ord_le2494988322063910608_state @ X2 @ Z2 ) ) ) ).
% le_inf_iff
thf(fact_1108_inf_Obounded__iff,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ ( inf_inf_set_state @ B3 @ C ) )
= ( ( ord_le2494988322063910608_state @ A2 @ B3 )
& ( ord_le2494988322063910608_state @ A2 @ C ) ) ) ).
% inf.bounded_iff
thf(fact_1109_Int__subset__iff,axiom,
! [C2: set_state,A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ C2 @ ( inf_inf_set_state @ A @ B ) )
= ( ( ord_le2494988322063910608_state @ C2 @ A )
& ( ord_le2494988322063910608_state @ C2 @ B ) ) ) ).
% Int_subset_iff
thf(fact_1110_Int__insert__right__if1,axiom,
! [A2: state,A: set_state,B: set_state] :
( ( member_state @ A2 @ A )
=> ( ( inf_inf_set_state @ A @ ( insert_state @ A2 @ B ) )
= ( insert_state @ A2 @ ( inf_inf_set_state @ A @ B ) ) ) ) ).
% Int_insert_right_if1
thf(fact_1111_Int__insert__right__if0,axiom,
! [A2: state,A: set_state,B: set_state] :
( ~ ( member_state @ A2 @ A )
=> ( ( inf_inf_set_state @ A @ ( insert_state @ A2 @ B ) )
= ( inf_inf_set_state @ A @ B ) ) ) ).
% Int_insert_right_if0
thf(fact_1112_Int__insert__left__if1,axiom,
! [A2: state,C2: set_state,B: set_state] :
( ( member_state @ A2 @ C2 )
=> ( ( inf_inf_set_state @ ( insert_state @ A2 @ B ) @ C2 )
= ( insert_state @ A2 @ ( inf_inf_set_state @ B @ C2 ) ) ) ) ).
% Int_insert_left_if1
thf(fact_1113_Int__insert__left__if0,axiom,
! [A2: state,C2: set_state,B: set_state] :
( ~ ( member_state @ A2 @ C2 )
=> ( ( inf_inf_set_state @ ( insert_state @ A2 @ B ) @ C2 )
= ( inf_inf_set_state @ B @ C2 ) ) ) ).
% Int_insert_left_if0
thf(fact_1114_insert__Diff1,axiom,
! [X2: state,B: set_state,A: set_state] :
( ( member_state @ X2 @ B )
=> ( ( minus_3933957440811877961_state @ ( insert_state @ X2 @ A ) @ B )
= ( minus_3933957440811877961_state @ A @ B ) ) ) ).
% insert_Diff1
thf(fact_1115_Diff__insert0,axiom,
! [X2: state,A: set_state,B: set_state] :
( ~ ( member_state @ X2 @ A )
=> ( ( minus_3933957440811877961_state @ A @ ( insert_state @ X2 @ B ) )
= ( minus_3933957440811877961_state @ A @ B ) ) ) ).
% Diff_insert0
thf(fact_1116_insert__disjoint_I1_J,axiom,
! [A2: state,A: set_state,B: set_state] :
( ( ( inf_inf_set_state @ ( insert_state @ A2 @ A ) @ B )
= bot_bot_set_state )
= ( ~ ( member_state @ A2 @ B )
& ( ( inf_inf_set_state @ A @ B )
= bot_bot_set_state ) ) ) ).
% insert_disjoint(1)
thf(fact_1117_insert__disjoint_I2_J,axiom,
! [A2: state,A: set_state,B: set_state] :
( ( bot_bot_set_state
= ( inf_inf_set_state @ ( insert_state @ A2 @ A ) @ B ) )
= ( ~ ( member_state @ A2 @ B )
& ( bot_bot_set_state
= ( inf_inf_set_state @ A @ B ) ) ) ) ).
% insert_disjoint(2)
thf(fact_1118_disjoint__insert_I1_J,axiom,
! [B: set_state,A2: state,A: set_state] :
( ( ( inf_inf_set_state @ B @ ( insert_state @ A2 @ A ) )
= bot_bot_set_state )
= ( ~ ( member_state @ A2 @ B )
& ( ( inf_inf_set_state @ B @ A )
= bot_bot_set_state ) ) ) ).
% disjoint_insert(1)
thf(fact_1119_disjoint__insert_I2_J,axiom,
! [A: set_state,B3: state,B: set_state] :
( ( bot_bot_set_state
= ( inf_inf_set_state @ A @ ( insert_state @ B3 @ B ) ) )
= ( ~ ( member_state @ B3 @ A )
& ( bot_bot_set_state
= ( inf_inf_set_state @ A @ B ) ) ) ) ).
% disjoint_insert(2)
thf(fact_1120_Diff__eq__empty__iff,axiom,
! [A: set_state,B: set_state] :
( ( ( minus_3933957440811877961_state @ A @ B )
= bot_bot_set_state )
= ( ord_le2494988322063910608_state @ A @ B ) ) ).
% Diff_eq_empty_iff
thf(fact_1121_disjoint__iff,axiom,
! [A: set_state,B: set_state] :
( ( ( inf_inf_set_state @ A @ B )
= bot_bot_set_state )
= ( ! [X3: state] :
( ( member_state @ X3 @ A )
=> ~ ( member_state @ X3 @ B ) ) ) ) ).
% disjoint_iff
thf(fact_1122_Int__emptyI,axiom,
! [A: set_state,B: set_state] :
( ! [X: state] :
( ( member_state @ X @ A )
=> ~ ( member_state @ X @ B ) )
=> ( ( inf_inf_set_state @ A @ B )
= bot_bot_set_state ) ) ).
% Int_emptyI
thf(fact_1123_Diff__mono,axiom,
! [A: set_state,C2: set_state,D2: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ C2 )
=> ( ( ord_le2494988322063910608_state @ D2 @ B )
=> ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A @ B ) @ ( minus_3933957440811877961_state @ C2 @ D2 ) ) ) ) ).
% Diff_mono
thf(fact_1124_Diff__subset,axiom,
! [A: set_state,B: set_state] : ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A @ B ) @ A ) ).
% Diff_subset
thf(fact_1125_double__diff,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( ord_le2494988322063910608_state @ B @ C2 )
=> ( ( minus_3933957440811877961_state @ B @ ( minus_3933957440811877961_state @ C2 @ A ) )
= A ) ) ) ).
% double_diff
thf(fact_1126_Int__mono,axiom,
! [A: set_state,C2: set_state,B: set_state,D2: set_state] :
( ( ord_le2494988322063910608_state @ A @ C2 )
=> ( ( ord_le2494988322063910608_state @ B @ D2 )
=> ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ ( inf_inf_set_state @ C2 @ D2 ) ) ) ) ).
% Int_mono
thf(fact_1127_Int__lower1,axiom,
! [A: set_state,B: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ A ) ).
% Int_lower1
thf(fact_1128_Int__lower2,axiom,
! [A: set_state,B: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ B ) @ B ) ).
% Int_lower2
thf(fact_1129_Int__absorb1,axiom,
! [B: set_state,A: set_state] :
( ( ord_le2494988322063910608_state @ B @ A )
=> ( ( inf_inf_set_state @ A @ B )
= B ) ) ).
% Int_absorb1
thf(fact_1130_Int__absorb2,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( inf_inf_set_state @ A @ B )
= A ) ) ).
% Int_absorb2
thf(fact_1131_Int__greatest,axiom,
! [C2: set_state,A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ C2 @ A )
=> ( ( ord_le2494988322063910608_state @ C2 @ B )
=> ( ord_le2494988322063910608_state @ C2 @ ( inf_inf_set_state @ A @ B ) ) ) ) ).
% Int_greatest
thf(fact_1132_Int__Collect__mono,axiom,
! [A: set_state,B: set_state,P: state > $o,Q: state > $o] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ! [X: state] :
( ( member_state @ X @ A )
=> ( ( P @ X )
=> ( Q @ X ) ) )
=> ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A @ ( collect_state @ P ) ) @ ( inf_inf_set_state @ B @ ( collect_state @ Q ) ) ) ) ) ).
% Int_Collect_mono
thf(fact_1133_inf__sup__ord_I2_J,axiom,
! [X2: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X2 @ Y ) @ Y ) ).
% inf_sup_ord(2)
thf(fact_1134_inf__sup__ord_I1_J,axiom,
! [X2: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X2 @ Y ) @ X2 ) ).
% inf_sup_ord(1)
thf(fact_1135_inf__le1,axiom,
! [X2: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X2 @ Y ) @ X2 ) ).
% inf_le1
thf(fact_1136_inf__le2,axiom,
! [X2: set_state,Y: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X2 @ Y ) @ Y ) ).
% inf_le2
thf(fact_1137_le__infE,axiom,
! [X2: set_state,A2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ ( inf_inf_set_state @ A2 @ B3 ) )
=> ~ ( ( ord_le2494988322063910608_state @ X2 @ A2 )
=> ~ ( ord_le2494988322063910608_state @ X2 @ B3 ) ) ) ).
% le_infE
thf(fact_1138_le__infI,axiom,
! [X2: set_state,A2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ A2 )
=> ( ( ord_le2494988322063910608_state @ X2 @ B3 )
=> ( ord_le2494988322063910608_state @ X2 @ ( inf_inf_set_state @ A2 @ B3 ) ) ) ) ).
% le_infI
thf(fact_1139_inf__mono,axiom,
! [A2: set_state,C: set_state,B3: set_state,D: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ C )
=> ( ( ord_le2494988322063910608_state @ B3 @ D )
=> ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A2 @ B3 ) @ ( inf_inf_set_state @ C @ D ) ) ) ) ).
% inf_mono
thf(fact_1140_le__infI1,axiom,
! [A2: set_state,X2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ X2 )
=> ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A2 @ B3 ) @ X2 ) ) ).
% le_infI1
thf(fact_1141_le__infI2,axiom,
! [B3: set_state,X2: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ X2 )
=> ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A2 @ B3 ) @ X2 ) ) ).
% le_infI2
thf(fact_1142_inf_OorderE,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( A2
= ( inf_inf_set_state @ A2 @ B3 ) ) ) ).
% inf.orderE
thf(fact_1143_inf_OorderI,axiom,
! [A2: set_state,B3: set_state] :
( ( A2
= ( inf_inf_set_state @ A2 @ B3 ) )
=> ( ord_le2494988322063910608_state @ A2 @ B3 ) ) ).
% inf.orderI
thf(fact_1144_inf__unique,axiom,
! [F: set_state > set_state > set_state,X2: set_state,Y: set_state] :
( ! [X: set_state,Y2: set_state] : ( ord_le2494988322063910608_state @ ( F @ X @ Y2 ) @ X )
=> ( ! [X: set_state,Y2: set_state] : ( ord_le2494988322063910608_state @ ( F @ X @ Y2 ) @ Y2 )
=> ( ! [X: set_state,Y2: set_state,Z3: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ( ord_le2494988322063910608_state @ X @ Z3 )
=> ( ord_le2494988322063910608_state @ X @ ( F @ Y2 @ Z3 ) ) ) )
=> ( ( inf_inf_set_state @ X2 @ Y )
= ( F @ X2 @ Y ) ) ) ) ) ).
% inf_unique
thf(fact_1145_le__iff__inf,axiom,
( ord_le2494988322063910608_state
= ( ^ [X3: set_state,Y4: set_state] :
( ( inf_inf_set_state @ X3 @ Y4 )
= X3 ) ) ) ).
% le_iff_inf
thf(fact_1146_inf_Oabsorb1,axiom,
! [A2: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( inf_inf_set_state @ A2 @ B3 )
= A2 ) ) ).
% inf.absorb1
thf(fact_1147_inf_Oabsorb2,axiom,
! [B3: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ A2 )
=> ( ( inf_inf_set_state @ A2 @ B3 )
= B3 ) ) ).
% inf.absorb2
thf(fact_1148_inf__absorb1,axiom,
! [X2: set_state,Y: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( inf_inf_set_state @ X2 @ Y )
= X2 ) ) ).
% inf_absorb1
thf(fact_1149_inf__absorb2,axiom,
! [Y: set_state,X2: set_state] :
( ( ord_le2494988322063910608_state @ Y @ X2 )
=> ( ( inf_inf_set_state @ X2 @ Y )
= Y ) ) ).
% inf_absorb2
thf(fact_1150_inf_OboundedE,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ ( inf_inf_set_state @ B3 @ C ) )
=> ~ ( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ~ ( ord_le2494988322063910608_state @ A2 @ C ) ) ) ).
% inf.boundedE
thf(fact_1151_inf_OboundedI,axiom,
! [A2: set_state,B3: set_state,C: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ B3 )
=> ( ( ord_le2494988322063910608_state @ A2 @ C )
=> ( ord_le2494988322063910608_state @ A2 @ ( inf_inf_set_state @ B3 @ C ) ) ) ) ).
% inf.boundedI
thf(fact_1152_inf__greatest,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( ord_le2494988322063910608_state @ X2 @ Z2 )
=> ( ord_le2494988322063910608_state @ X2 @ ( inf_inf_set_state @ Y @ Z2 ) ) ) ) ).
% inf_greatest
thf(fact_1153_inf_Oorder__iff,axiom,
( ord_le2494988322063910608_state
= ( ^ [A4: set_state,B4: set_state] :
( A4
= ( inf_inf_set_state @ A4 @ B4 ) ) ) ) ).
% inf.order_iff
thf(fact_1154_inf_Ocobounded1,axiom,
! [A2: set_state,B3: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A2 @ B3 ) @ A2 ) ).
% inf.cobounded1
thf(fact_1155_inf_Ocobounded2,axiom,
! [A2: set_state,B3: set_state] : ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A2 @ B3 ) @ B3 ) ).
% inf.cobounded2
thf(fact_1156_inf_Oabsorb__iff1,axiom,
( ord_le2494988322063910608_state
= ( ^ [A4: set_state,B4: set_state] :
( ( inf_inf_set_state @ A4 @ B4 )
= A4 ) ) ) ).
% inf.absorb_iff1
thf(fact_1157_inf_Oabsorb__iff2,axiom,
( ord_le2494988322063910608_state
= ( ^ [B4: set_state,A4: set_state] :
( ( inf_inf_set_state @ A4 @ B4 )
= B4 ) ) ) ).
% inf.absorb_iff2
thf(fact_1158_inf_OcoboundedI1,axiom,
! [A2: set_state,C: set_state,B3: set_state] :
( ( ord_le2494988322063910608_state @ A2 @ C )
=> ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A2 @ B3 ) @ C ) ) ).
% inf.coboundedI1
thf(fact_1159_inf_OcoboundedI2,axiom,
! [B3: set_state,C: set_state,A2: set_state] :
( ( ord_le2494988322063910608_state @ B3 @ C )
=> ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ A2 @ B3 ) @ C ) ) ).
% inf.coboundedI2
thf(fact_1160_Int__insert__right,axiom,
! [A2: state,A: set_state,B: set_state] :
( ( ( member_state @ A2 @ A )
=> ( ( inf_inf_set_state @ A @ ( insert_state @ A2 @ B ) )
= ( insert_state @ A2 @ ( inf_inf_set_state @ A @ B ) ) ) )
& ( ~ ( member_state @ A2 @ A )
=> ( ( inf_inf_set_state @ A @ ( insert_state @ A2 @ B ) )
= ( inf_inf_set_state @ A @ B ) ) ) ) ).
% Int_insert_right
thf(fact_1161_Int__insert__left,axiom,
! [A2: state,C2: set_state,B: set_state] :
( ( ( member_state @ A2 @ C2 )
=> ( ( inf_inf_set_state @ ( insert_state @ A2 @ B ) @ C2 )
= ( insert_state @ A2 @ ( inf_inf_set_state @ B @ C2 ) ) ) )
& ( ~ ( member_state @ A2 @ C2 )
=> ( ( inf_inf_set_state @ ( insert_state @ A2 @ B ) @ C2 )
= ( inf_inf_set_state @ B @ C2 ) ) ) ) ).
% Int_insert_left
thf(fact_1162_insert__Diff__if,axiom,
! [X2: state,B: set_state,A: set_state] :
( ( ( member_state @ X2 @ B )
=> ( ( minus_3933957440811877961_state @ ( insert_state @ X2 @ A ) @ B )
= ( minus_3933957440811877961_state @ A @ B ) ) )
& ( ~ ( member_state @ X2 @ B )
=> ( ( minus_3933957440811877961_state @ ( insert_state @ X2 @ A ) @ B )
= ( insert_state @ X2 @ ( minus_3933957440811877961_state @ A @ B ) ) ) ) ) ).
% insert_Diff_if
thf(fact_1163_psubset__imp__ex__mem,axiom,
! [A: set_state,B: set_state] :
( ( ord_less_set_state @ A @ B )
=> ? [B5: state] : ( member_state @ B5 @ ( minus_3933957440811877961_state @ B @ A ) ) ) ).
% psubset_imp_ex_mem
thf(fact_1164_IntE,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( inf_inf_set_state @ A @ B ) )
=> ~ ( ( member_state @ C @ A )
=> ~ ( member_state @ C @ B ) ) ) ).
% IntE
thf(fact_1165_DiffE,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( minus_3933957440811877961_state @ A @ B ) )
=> ~ ( ( member_state @ C @ A )
=> ( member_state @ C @ B ) ) ) ).
% DiffE
thf(fact_1166_IntD1,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( inf_inf_set_state @ A @ B ) )
=> ( member_state @ C @ A ) ) ).
% IntD1
thf(fact_1167_IntD2,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( inf_inf_set_state @ A @ B ) )
=> ( member_state @ C @ B ) ) ).
% IntD2
thf(fact_1168_DiffD1,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( minus_3933957440811877961_state @ A @ B ) )
=> ( member_state @ C @ A ) ) ).
% DiffD1
thf(fact_1169_DiffD2,axiom,
! [C: state,A: set_state,B: set_state] :
( ( member_state @ C @ ( minus_3933957440811877961_state @ A @ B ) )
=> ~ ( member_state @ C @ B ) ) ).
% DiffD2
thf(fact_1170_distrib__inf__le,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] : ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ ( inf_inf_set_state @ X2 @ Y ) @ ( inf_inf_set_state @ X2 @ Z2 ) ) @ ( inf_inf_set_state @ X2 @ ( sup_sup_set_state @ Y @ Z2 ) ) ) ).
% distrib_inf_le
thf(fact_1171_distrib__sup__le,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] : ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ X2 @ ( inf_inf_set_state @ Y @ Z2 ) ) @ ( inf_inf_set_state @ ( sup_sup_set_state @ X2 @ Y ) @ ( sup_sup_set_state @ X2 @ Z2 ) ) ) ).
% distrib_sup_le
thf(fact_1172_diff__shunt__var,axiom,
! [X2: set_state,Y: set_state] :
( ( ( minus_3933957440811877961_state @ X2 @ Y )
= bot_bot_set_state )
= ( ord_le2494988322063910608_state @ X2 @ Y ) ) ).
% diff_shunt_var
thf(fact_1173_Diff__insert__absorb,axiom,
! [X2: state,A: set_state] :
( ~ ( member_state @ X2 @ A )
=> ( ( minus_3933957440811877961_state @ ( insert_state @ X2 @ A ) @ ( insert_state @ X2 @ bot_bot_set_state ) )
= A ) ) ).
% Diff_insert_absorb
thf(fact_1174_insert__Diff,axiom,
! [A2: state,A: set_state] :
( ( member_state @ A2 @ A )
=> ( ( insert_state @ A2 @ ( minus_3933957440811877961_state @ A @ ( insert_state @ A2 @ bot_bot_set_state ) ) )
= A ) ) ).
% insert_Diff
thf(fact_1175_subset__Diff__insert,axiom,
! [A: set_state,B: set_state,X2: state,C2: set_state] :
( ( ord_le2494988322063910608_state @ A @ ( minus_3933957440811877961_state @ B @ ( insert_state @ X2 @ C2 ) ) )
= ( ( ord_le2494988322063910608_state @ A @ ( minus_3933957440811877961_state @ B @ C2 ) )
& ~ ( member_state @ X2 @ A ) ) ) ).
% subset_Diff_insert
thf(fact_1176_Un__Int__assoc__eq,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( ( sup_sup_set_state @ ( inf_inf_set_state @ A @ B ) @ C2 )
= ( inf_inf_set_state @ A @ ( sup_sup_set_state @ B @ C2 ) ) )
= ( ord_le2494988322063910608_state @ C2 @ A ) ) ).
% Un_Int_assoc_eq
thf(fact_1177_Diff__partition,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ( sup_sup_set_state @ A @ ( minus_3933957440811877961_state @ B @ A ) )
= B ) ) ).
% Diff_partition
thf(fact_1178_Diff__subset__conv,axiom,
! [A: set_state,B: set_state,C2: set_state] :
( ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A @ B ) @ C2 )
= ( ord_le2494988322063910608_state @ A @ ( sup_sup_set_state @ B @ C2 ) ) ) ).
% Diff_subset_conv
thf(fact_1179_inf__shunt,axiom,
! [X2: set_state,Y: set_state] :
( ( ( inf_inf_set_state @ X2 @ Y )
= bot_bot_set_state )
= ( ord_le2494988322063910608_state @ X2 @ ( uminus472742206872269241_state @ Y ) ) ) ).
% inf_shunt
thf(fact_1180_sup__neg__inf,axiom,
! [P2: set_state,Q2: set_state,R3: set_state] :
( ( ord_le2494988322063910608_state @ P2 @ ( sup_sup_set_state @ Q2 @ R3 ) )
= ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ P2 @ ( uminus472742206872269241_state @ Q2 ) ) @ R3 ) ) ).
% sup_neg_inf
thf(fact_1181_shunt2,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X2 @ ( uminus472742206872269241_state @ Y ) ) @ Z2 )
= ( ord_le2494988322063910608_state @ X2 @ ( sup_sup_set_state @ Y @ Z2 ) ) ) ).
% shunt2
thf(fact_1182_shunt1,axiom,
! [X2: set_state,Y: set_state,Z2: set_state] :
( ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ X2 @ Y ) @ Z2 )
= ( ord_le2494988322063910608_state @ X2 @ ( sup_sup_set_state @ ( uminus472742206872269241_state @ Y ) @ Z2 ) ) ) ).
% shunt1
thf(fact_1183_less__eq__Inf__inter,axiom,
! [A: set_set_state,B: set_set_state] : ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ ( comple1177038664686533161_state @ A ) @ ( comple1177038664686533161_state @ B ) ) @ ( comple1177038664686533161_state @ ( inf_in8939913482472430008_state @ A @ B ) ) ) ).
% less_eq_Inf_inter
thf(fact_1184_Diff__single__insert,axiom,
! [A: set_state,X2: state,B: set_state] :
( ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A @ ( insert_state @ X2 @ bot_bot_set_state ) ) @ B )
=> ( ord_le2494988322063910608_state @ A @ ( insert_state @ X2 @ B ) ) ) ).
% Diff_single_insert
thf(fact_1185_subset__insert__iff,axiom,
! [A: set_state,X2: state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ ( insert_state @ X2 @ B ) )
= ( ( ( member_state @ X2 @ A )
=> ( ord_le2494988322063910608_state @ ( minus_3933957440811877961_state @ A @ ( insert_state @ X2 @ bot_bot_set_state ) ) @ B ) )
& ( ~ ( member_state @ X2 @ A )
=> ( ord_le2494988322063910608_state @ A @ B ) ) ) ) ).
% subset_insert_iff
thf(fact_1186_disjoint__eq__subset__Compl,axiom,
! [A: set_state,B: set_state] :
( ( ( inf_inf_set_state @ A @ B )
= bot_bot_set_state )
= ( ord_le2494988322063910608_state @ A @ ( uminus472742206872269241_state @ B ) ) ) ).
% disjoint_eq_subset_Compl
thf(fact_1187_Inter__Un__subset,axiom,
! [A: set_set_state,B: set_set_state] : ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ ( comple1177038664686533161_state @ A ) @ ( comple1177038664686533161_state @ B ) ) @ ( comple1177038664686533161_state @ ( inf_in8939913482472430008_state @ A @ B ) ) ) ).
% Inter_Un_subset
thf(fact_1188_psubset__insert__iff,axiom,
! [A: set_state,X2: state,B: set_state] :
( ( ord_less_set_state @ A @ ( insert_state @ X2 @ B ) )
= ( ( ( member_state @ X2 @ B )
=> ( ord_less_set_state @ A @ B ) )
& ( ~ ( member_state @ X2 @ B )
=> ( ( ( member_state @ X2 @ A )
=> ( ord_less_set_state @ ( minus_3933957440811877961_state @ A @ ( insert_state @ X2 @ bot_bot_set_state ) ) @ B ) )
& ( ~ ( member_state @ X2 @ A )
=> ( ord_le2494988322063910608_state @ A @ B ) ) ) ) ) ) ).
% psubset_insert_iff
thf(fact_1189_inf__top_Osemilattice__neutr__order__axioms,axiom,
semila3858001251800985922_state @ inf_inf_set_state @ top_top_set_state @ ord_le2494988322063910608_state @ ord_less_set_state ).
% inf_top.semilattice_neutr_order_axioms
thf(fact_1190_less__eq__cInf__inter,axiom,
! [A: set_set_state,B: set_set_state] :
( ( condit9136120872139659296_state @ A )
=> ( ( condit9136120872139659296_state @ B )
=> ( ( ( inf_in8939913482472430008_state @ A @ B )
!= bot_bo2271482359692755898_state )
=> ( ord_le2494988322063910608_state @ ( inf_inf_set_state @ ( comple1177038664686533161_state @ A ) @ ( comple1177038664686533161_state @ B ) ) @ ( comple1177038664686533161_state @ ( inf_in8939913482472430008_state @ A @ B ) ) ) ) ) ) ).
% less_eq_cInf_inter
thf(fact_1191_member__remove,axiom,
! [X2: state,Y: state,A: set_state] :
( ( member_state @ X2 @ ( remove_state @ Y @ A ) )
= ( ( member_state @ X2 @ A )
& ( X2 != Y ) ) ) ).
% member_remove
thf(fact_1192_bdd__belowI,axiom,
! [A: set_set_state,M: set_state] :
( ! [X: set_state] :
( ( member_set_state @ X @ A )
=> ( ord_le2494988322063910608_state @ M @ X ) )
=> ( condit9136120872139659296_state @ A ) ) ).
% bdd_belowI
thf(fact_1193_bdd__below_OI,axiom,
! [A: set_set_state,M2: set_state] :
( ! [X: set_state] :
( ( member_set_state @ X @ A )
=> ( ord_le2494988322063910608_state @ M2 @ X ) )
=> ( condit9136120872139659296_state @ A ) ) ).
% bdd_below.I
thf(fact_1194_bdd__below_OE,axiom,
! [A: set_set_state] :
( ( condit9136120872139659296_state @ A )
=> ~ ! [M3: set_state] :
~ ! [X6: set_state] :
( ( member_set_state @ X6 @ A )
=> ( ord_le2494988322063910608_state @ M3 @ X6 ) ) ) ).
% bdd_below.E
thf(fact_1195_bdd__below_Ounfold,axiom,
( condit9136120872139659296_state
= ( ^ [A3: set_set_state] :
? [M4: set_state] :
! [X3: set_state] :
( ( member_set_state @ X3 @ A3 )
=> ( ord_le2494988322063910608_state @ M4 @ X3 ) ) ) ) ).
% bdd_below.unfold
thf(fact_1196_cInf__lower2,axiom,
! [X2: set_state,X5: set_set_state,Y: set_state] :
( ( member_set_state @ X2 @ X5 )
=> ( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ( condit9136120872139659296_state @ X5 )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ X5 ) @ Y ) ) ) ) ).
% cInf_lower2
thf(fact_1197_cInf__lower,axiom,
! [X2: set_state,X5: set_set_state] :
( ( member_set_state @ X2 @ X5 )
=> ( ( condit9136120872139659296_state @ X5 )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ X5 ) @ X2 ) ) ) ).
% cInf_lower
thf(fact_1198_le__cInf__iff,axiom,
! [S: set_set_state,A2: set_state] :
( ( S != bot_bo2271482359692755898_state )
=> ( ( condit9136120872139659296_state @ S )
=> ( ( ord_le2494988322063910608_state @ A2 @ ( comple1177038664686533161_state @ S ) )
= ( ! [X3: set_state] :
( ( member_set_state @ X3 @ S )
=> ( ord_le2494988322063910608_state @ A2 @ X3 ) ) ) ) ) ) ).
% le_cInf_iff
thf(fact_1199_cInf__mono,axiom,
! [B: set_set_state,A: set_set_state] :
( ( B != bot_bo2271482359692755898_state )
=> ( ( condit9136120872139659296_state @ A )
=> ( ! [B5: set_state] :
( ( member_set_state @ B5 @ B )
=> ? [X6: set_state] :
( ( member_set_state @ X6 @ A )
& ( ord_le2494988322063910608_state @ X6 @ B5 ) ) )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ A ) @ ( comple1177038664686533161_state @ B ) ) ) ) ) ).
% cInf_mono
thf(fact_1200_cInf__superset__mono,axiom,
! [A: set_set_state,B: set_set_state] :
( ( A != bot_bo2271482359692755898_state )
=> ( ( condit9136120872139659296_state @ B )
=> ( ( ord_le5175021213330142598_state @ A @ B )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ B ) @ ( comple1177038664686533161_state @ A ) ) ) ) ) ).
% cInf_superset_mono
thf(fact_1201_image__eqI,axiom,
! [B3: state,F: state > state,X2: state,A: set_state] :
( ( B3
= ( F @ X2 ) )
=> ( ( member_state @ X2 @ A )
=> ( member_state @ B3 @ ( image_state_state @ F @ A ) ) ) ) ).
% image_eqI
thf(fact_1202_bdd__belowI2,axiom,
! [A: set_state,M: set_state,F: state > set_state] :
( ! [X: state] :
( ( member_state @ X @ A )
=> ( ord_le2494988322063910608_state @ M @ ( F @ X ) ) )
=> ( condit9136120872139659296_state @ ( image_4774290769506072625_state @ F @ A ) ) ) ).
% bdd_belowI2
thf(fact_1203_bdd__below_OI2,axiom,
! [A: set_state,M2: set_state,F: state > set_state] :
( ! [X: state] :
( ( member_state @ X @ A )
=> ( ord_le2494988322063910608_state @ M2 @ ( F @ X ) ) )
=> ( condit9136120872139659296_state @ ( image_4774290769506072625_state @ F @ A ) ) ) ).
% bdd_below.I2
thf(fact_1204_INF__eq,axiom,
! [A: set_state,B: set_state,G2: state > set_state,F: state > set_state] :
( ! [I2: state] :
( ( member_state @ I2 @ A )
=> ? [X6: state] :
( ( member_state @ X6 @ B )
& ( ord_le2494988322063910608_state @ ( G2 @ X6 ) @ ( F @ I2 ) ) ) )
=> ( ! [J: state] :
( ( member_state @ J @ B )
=> ? [X6: state] :
( ( member_state @ X6 @ A )
& ( ord_le2494988322063910608_state @ ( F @ X6 ) @ ( G2 @ J ) ) ) )
=> ( ( comple1177038664686533161_state @ ( image_4774290769506072625_state @ F @ A ) )
= ( comple1177038664686533161_state @ ( image_4774290769506072625_state @ G2 @ B ) ) ) ) ) ).
% INF_eq
thf(fact_1205_image__mono,axiom,
! [A: set_state,B: set_state,F: state > state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A ) @ ( image_state_state @ F @ B ) ) ) ).
% image_mono
thf(fact_1206_image__subsetI,axiom,
! [A: set_state,F: state > state,B: set_state] :
( ! [X: state] :
( ( member_state @ X @ A )
=> ( member_state @ ( F @ X ) @ B ) )
=> ( ord_le2494988322063910608_state @ ( image_state_state @ F @ A ) @ B ) ) ).
% image_subsetI
thf(fact_1207_subset__imageE,axiom,
! [B: set_state,F: state > state,A: set_state] :
( ( ord_le2494988322063910608_state @ B @ ( image_state_state @ F @ A ) )
=> ~ ! [C6: set_state] :
( ( ord_le2494988322063910608_state @ C6 @ A )
=> ( B
!= ( image_state_state @ F @ C6 ) ) ) ) ).
% subset_imageE
thf(fact_1208_subset__image__iff,axiom,
! [B: set_state,F: state > state,A: set_state] :
( ( ord_le2494988322063910608_state @ B @ ( image_state_state @ F @ A ) )
= ( ? [AA: set_state] :
( ( ord_le2494988322063910608_state @ AA @ A )
& ( B
= ( image_state_state @ F @ AA ) ) ) ) ) ).
% subset_image_iff
thf(fact_1209_imageI,axiom,
! [X2: state,A: set_state,F: state > state] :
( ( member_state @ X2 @ A )
=> ( member_state @ ( F @ X2 ) @ ( image_state_state @ F @ A ) ) ) ).
% imageI
thf(fact_1210_rev__image__eqI,axiom,
! [X2: state,A: set_state,B3: state,F: state > state] :
( ( member_state @ X2 @ A )
=> ( ( B3
= ( F @ X2 ) )
=> ( member_state @ B3 @ ( image_state_state @ F @ A ) ) ) ) ).
% rev_image_eqI
thf(fact_1211_INF__eq__iff,axiom,
! [I4: set_state,F: state > set_state,C: set_state] :
( ( I4 != bot_bot_set_state )
=> ( ! [I2: state] :
( ( member_state @ I2 @ I4 )
=> ( ord_le2494988322063910608_state @ ( F @ I2 ) @ C ) )
=> ( ( ( comple1177038664686533161_state @ ( image_4774290769506072625_state @ F @ I4 ) )
= C )
= ( ! [X3: state] :
( ( member_state @ X3 @ I4 )
=> ( ( F @ X3 )
= C ) ) ) ) ) ) ).
% INF_eq_iff
thf(fact_1212_cINF__greatest,axiom,
! [A: set_state,M: set_state,F: state > set_state] :
( ( A != bot_bot_set_state )
=> ( ! [X: state] :
( ( member_state @ X @ A )
=> ( ord_le2494988322063910608_state @ M @ ( F @ X ) ) )
=> ( ord_le2494988322063910608_state @ M @ ( comple1177038664686533161_state @ ( image_4774290769506072625_state @ F @ A ) ) ) ) ) ).
% cINF_greatest
thf(fact_1213_in__image__insert__iff,axiom,
! [B: set_set_state,X2: state,A: set_state] :
( ! [C6: set_state] :
( ( member_set_state @ C6 @ B )
=> ~ ( member_state @ X2 @ C6 ) )
=> ( ( member_set_state @ A @ ( image_2476256681063834599_state @ ( insert_state @ X2 ) @ B ) )
= ( ( member_state @ X2 @ A )
& ( member_set_state @ ( minus_3933957440811877961_state @ A @ ( insert_state @ X2 @ bot_bot_set_state ) ) @ B ) ) ) ) ).
% in_image_insert_iff
thf(fact_1214_cINF__lower,axiom,
! [F: state > set_state,A: set_state,X2: state] :
( ( condit9136120872139659296_state @ ( image_4774290769506072625_state @ F @ A ) )
=> ( ( member_state @ X2 @ A )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ ( image_4774290769506072625_state @ F @ A ) ) @ ( F @ X2 ) ) ) ) ).
% cINF_lower
thf(fact_1215_cINF__lower2,axiom,
! [F: state > set_state,A: set_state,X2: state,U: set_state] :
( ( condit9136120872139659296_state @ ( image_4774290769506072625_state @ F @ A ) )
=> ( ( member_state @ X2 @ A )
=> ( ( ord_le2494988322063910608_state @ ( F @ X2 ) @ U )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ ( image_4774290769506072625_state @ F @ A ) ) @ U ) ) ) ) ).
% cINF_lower2
thf(fact_1216_cINF__superset__mono,axiom,
! [A: set_state,G2: state > set_state,B: set_state,F: state > set_state] :
( ( A != bot_bot_set_state )
=> ( ( condit9136120872139659296_state @ ( image_4774290769506072625_state @ G2 @ B ) )
=> ( ( ord_le2494988322063910608_state @ A @ B )
=> ( ! [X: state] :
( ( member_state @ X @ B )
=> ( ord_le2494988322063910608_state @ ( G2 @ X ) @ ( F @ X ) ) )
=> ( ord_le2494988322063910608_state @ ( comple1177038664686533161_state @ ( image_4774290769506072625_state @ G2 @ B ) ) @ ( comple1177038664686533161_state @ ( image_4774290769506072625_state @ F @ A ) ) ) ) ) ) ) ).
% cINF_superset_mono
thf(fact_1217_all__subset__image,axiom,
! [F: state > state,A: set_state,P: set_state > $o] :
( ( ! [B2: set_state] :
( ( ord_le2494988322063910608_state @ B2 @ ( image_state_state @ F @ A ) )
=> ( P @ B2 ) ) )
= ( ! [B2: set_state] :
( ( ord_le2494988322063910608_state @ B2 @ A )
=> ( P @ ( image_state_state @ F @ B2 ) ) ) ) ) ).
% all_subset_image
thf(fact_1218_Fpow__mono,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ord_le5175021213330142598_state @ ( finite_Fpow_state @ A ) @ ( finite_Fpow_state @ B ) ) ) ).
% Fpow_mono
thf(fact_1219_mono__image__least,axiom,
! [F: set_state > set_state,M: set_state,N: set_state,M5: set_state,N2: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( ( image_2476256681063834599_state @ F @ ( set_or2838015025653527455_state @ M @ N ) )
= ( set_or2838015025653527455_state @ M5 @ N2 ) )
=> ( ( ord_less_set_state @ M @ N )
=> ( ( F @ M )
= M5 ) ) ) ) ).
% mono_image_least
thf(fact_1220_PowI,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( member_set_state @ A @ ( pow_state @ B ) ) ) ).
% PowI
thf(fact_1221_Pow__iff,axiom,
! [A: set_state,B: set_state] :
( ( member_set_state @ A @ ( pow_state @ B ) )
= ( ord_le2494988322063910608_state @ A @ B ) ) ).
% Pow_iff
thf(fact_1222_PowD,axiom,
! [A: set_state,B: set_state] :
( ( member_set_state @ A @ ( pow_state @ B ) )
=> ( ord_le2494988322063910608_state @ A @ B ) ) ).
% PowD
thf(fact_1223_Pow__mono,axiom,
! [A: set_state,B: set_state] :
( ( ord_le2494988322063910608_state @ A @ B )
=> ( ord_le5175021213330142598_state @ ( pow_state @ A ) @ ( pow_state @ B ) ) ) ).
% Pow_mono
thf(fact_1224_strict__mono__mono,axiom,
! [F: set_state > set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_less_set_state @ ord_less_set_state @ F )
=> ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F ) ) ).
% strict_mono_mono
thf(fact_1225_mono__inf,axiom,
! [F: set_state > set_state,A: set_state,B: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ord_le2494988322063910608_state @ ( F @ ( inf_inf_set_state @ A @ B ) ) @ ( inf_inf_set_state @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% mono_inf
thf(fact_1226_mono__sup,axiom,
! [F: set_state > set_state,A: set_state,B: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ ( F @ A ) @ ( F @ B ) ) @ ( F @ ( sup_sup_set_state @ A @ B ) ) ) ) ).
% mono_sup
thf(fact_1227_mono__Int,axiom,
! [F: set_state > set_state,A: set_state,B: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ord_le2494988322063910608_state @ ( F @ ( inf_inf_set_state @ A @ B ) ) @ ( inf_inf_set_state @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% mono_Int
thf(fact_1228_mono__Un,axiom,
! [F: set_state > set_state,A: set_state,B: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ ( F @ A ) @ ( F @ B ) ) @ ( F @ ( sup_sup_set_state @ A @ B ) ) ) ) ).
% mono_Un
thf(fact_1229_ord_Omono__onD,axiom,
! [A: set_state,Less_eq2: state > state > $o,F: state > set_state,R3: state,S3: state] :
( ( monoto271350166776559507_state @ A @ Less_eq2 @ ord_le2494988322063910608_state @ F )
=> ( ( member_state @ R3 @ A )
=> ( ( member_state @ S3 @ A )
=> ( ( Less_eq2 @ R3 @ S3 )
=> ( ord_le2494988322063910608_state @ ( F @ R3 ) @ ( F @ S3 ) ) ) ) ) ) ).
% ord.mono_onD
thf(fact_1230_ord_Omono__onI,axiom,
! [A: set_state,Less_eq2: state > state > $o,F: state > set_state] :
( ! [R4: state,S4: state] :
( ( member_state @ R4 @ A )
=> ( ( member_state @ S4 @ A )
=> ( ( Less_eq2 @ R4 @ S4 )
=> ( ord_le2494988322063910608_state @ ( F @ R4 ) @ ( F @ S4 ) ) ) ) )
=> ( monoto271350166776559507_state @ A @ Less_eq2 @ ord_le2494988322063910608_state @ F ) ) ).
% ord.mono_onI
thf(fact_1231_ord_Omono__on__def,axiom,
! [A: set_state,Less_eq2: state > state > $o,F: state > set_state] :
( ( monoto271350166776559507_state @ A @ Less_eq2 @ ord_le2494988322063910608_state @ F )
= ( ! [R5: state,S5: state] :
( ( ( member_state @ R5 @ A )
& ( member_state @ S5 @ A )
& ( Less_eq2 @ R5 @ S5 ) )
=> ( ord_le2494988322063910608_state @ ( F @ R5 ) @ ( F @ S5 ) ) ) ) ) ).
% ord.mono_on_def
thf(fact_1232_mono__onD,axiom,
! [A: set_set_state,F: set_state > set_state,R3: set_state,S3: set_state] :
( ( monoto160555381311970121_state @ A @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( member_set_state @ R3 @ A )
=> ( ( member_set_state @ S3 @ A )
=> ( ( ord_le2494988322063910608_state @ R3 @ S3 )
=> ( ord_le2494988322063910608_state @ ( F @ R3 ) @ ( F @ S3 ) ) ) ) ) ) ).
% mono_onD
thf(fact_1233_mono__onI,axiom,
! [A: set_set_state,F: set_state > set_state] :
( ! [R4: set_state,S4: set_state] :
( ( member_set_state @ R4 @ A )
=> ( ( member_set_state @ S4 @ A )
=> ( ( ord_le2494988322063910608_state @ R4 @ S4 )
=> ( ord_le2494988322063910608_state @ ( F @ R4 ) @ ( F @ S4 ) ) ) ) )
=> ( monoto160555381311970121_state @ A @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F ) ) ).
% mono_onI
thf(fact_1234_ord_Omono__on__subset,axiom,
! [A: set_state,Less_eq2: state > state > $o,F: state > set_state,B: set_state] :
( ( monoto271350166776559507_state @ A @ Less_eq2 @ ord_le2494988322063910608_state @ F )
=> ( ( ord_le2494988322063910608_state @ B @ A )
=> ( monoto271350166776559507_state @ B @ Less_eq2 @ ord_le2494988322063910608_state @ F ) ) ) ).
% ord.mono_on_subset
thf(fact_1235_mono__on__subset,axiom,
! [A: set_set_state,F: set_state > set_state,B: set_set_state] :
( ( monoto160555381311970121_state @ A @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( ord_le5175021213330142598_state @ B @ A )
=> ( monoto160555381311970121_state @ B @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F ) ) ) ).
% mono_on_subset
thf(fact_1236_mono__imp__mono__on,axiom,
! [F: set_state > set_state,A: set_set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( monoto160555381311970121_state @ A @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F ) ) ).
% mono_imp_mono_on
thf(fact_1237_monoI,axiom,
! [F: set_state > set_state] :
( ! [X: set_state,Y2: set_state] :
( ( ord_le2494988322063910608_state @ X @ Y2 )
=> ( ord_le2494988322063910608_state @ ( F @ X ) @ ( F @ Y2 ) ) )
=> ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F ) ) ).
% monoI
thf(fact_1238_monoE,axiom,
! [F: set_state > set_state,X2: set_state,Y: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ord_le2494988322063910608_state @ ( F @ X2 ) @ ( F @ Y ) ) ) ) ).
% monoE
thf(fact_1239_monoD,axiom,
! [F: set_state > set_state,X2: set_state,Y: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( ord_le2494988322063910608_state @ X2 @ Y )
=> ( ord_le2494988322063910608_state @ ( F @ X2 ) @ ( F @ Y ) ) ) ) ).
% monoD
thf(fact_1240_bdd__below__image__mono,axiom,
! [F: set_state > set_state,A: set_set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( condit9136120872139659296_state @ A )
=> ( condit9136120872139659296_state @ ( image_2476256681063834599_state @ F @ A ) ) ) ) ).
% bdd_below_image_mono
thf(fact_1241_def__lfp__induct,axiom,
! [A: set_state,F: set_state > set_state,P: set_state] :
( ( A
= ( comple5794554108862647415_state @ F ) )
=> ( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( ord_le2494988322063910608_state @ ( F @ ( inf_inf_set_state @ A @ P ) ) @ P )
=> ( ord_le2494988322063910608_state @ A @ P ) ) ) ) ).
% def_lfp_induct
thf(fact_1242_lfp__induct,axiom,
! [F: set_state > set_state,P: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( ord_le2494988322063910608_state @ ( F @ ( inf_inf_set_state @ ( comple5794554108862647415_state @ F ) @ P ) ) @ P )
=> ( ord_le2494988322063910608_state @ ( comple5794554108862647415_state @ F ) @ P ) ) ) ).
% lfp_induct
thf(fact_1243_lfp__greatest,axiom,
! [F: set_state > set_state,A: set_state] :
( ! [U2: set_state] :
( ( ord_le2494988322063910608_state @ ( F @ U2 ) @ U2 )
=> ( ord_le2494988322063910608_state @ A @ U2 ) )
=> ( ord_le2494988322063910608_state @ A @ ( comple5794554108862647415_state @ F ) ) ) ).
% lfp_greatest
thf(fact_1244_lfp__lowerbound,axiom,
! [F: set_state > set_state,A: set_state] :
( ( ord_le2494988322063910608_state @ ( F @ A ) @ A )
=> ( ord_le2494988322063910608_state @ ( comple5794554108862647415_state @ F ) @ A ) ) ).
% lfp_lowerbound
thf(fact_1245_lfp__mono,axiom,
! [F: set_state > set_state,G2: set_state > set_state] :
( ! [Z4: set_state] : ( ord_le2494988322063910608_state @ ( F @ Z4 ) @ ( G2 @ Z4 ) )
=> ( ord_le2494988322063910608_state @ ( comple5794554108862647415_state @ F ) @ ( comple5794554108862647415_state @ G2 ) ) ) ).
% lfp_mono
thf(fact_1246_def__lfp__unfold,axiom,
! [H: set_state,F: set_state > set_state] :
( ( H
= ( comple5794554108862647415_state @ F ) )
=> ( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( H
= ( F @ H ) ) ) ) ).
% def_lfp_unfold
thf(fact_1247_lfp__fixpoint,axiom,
! [F: set_state > set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( F @ ( comple5794554108862647415_state @ F ) )
= ( comple5794554108862647415_state @ F ) ) ) ).
% lfp_fixpoint
thf(fact_1248_lfp__unfold,axiom,
! [F: set_state > set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( comple5794554108862647415_state @ F )
= ( F @ ( comple5794554108862647415_state @ F ) ) ) ) ).
% lfp_unfold
thf(fact_1249_lfp__eqI,axiom,
! [F3: set_state > set_state,X2: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F3 )
=> ( ( ( F3 @ X2 )
= X2 )
=> ( ! [Z3: set_state] :
( ( ( F3 @ Z3 )
= Z3 )
=> ( ord_le2494988322063910608_state @ X2 @ Z3 ) )
=> ( ( comple5794554108862647415_state @ F3 )
= X2 ) ) ) ) ).
% lfp_eqI
thf(fact_1250_chains__extend,axiom,
! [C: set_set_state,S: set_set_state,Z2: set_state] :
( ( member_set_set_state @ C @ ( chains_state @ S ) )
=> ( ( member_set_state @ Z2 @ S )
=> ( ! [X: set_state] :
( ( member_set_state @ X @ C )
=> ( ord_le2494988322063910608_state @ X @ Z2 ) )
=> ( member_set_set_state @ ( sup_su4188871578264421970_state @ ( insert_set_state @ Z2 @ bot_bo2271482359692755898_state ) @ C ) @ ( chains_state @ S ) ) ) ) ) ).
% chains_extend
thf(fact_1251_lfp__le__gfp,axiom,
! [F: set_state > set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ord_le2494988322063910608_state @ ( comple5794554108862647415_state @ F ) @ ( comple8759115402146780658_state @ F ) ) ) ).
% lfp_le_gfp
thf(fact_1252_weak__coinduct__image,axiom,
! [A2: state,X5: set_state,G2: state > state,F: set_state > set_state] :
( ( member_state @ A2 @ X5 )
=> ( ( ord_le2494988322063910608_state @ ( image_state_state @ G2 @ X5 ) @ ( F @ ( image_state_state @ G2 @ X5 ) ) )
=> ( member_state @ ( G2 @ A2 ) @ ( comple8759115402146780658_state @ F ) ) ) ) ).
% weak_coinduct_image
thf(fact_1253_Zorn__Lemma2,axiom,
! [A: set_set_state] :
( ! [X: set_set_state] :
( ( member_set_set_state @ X @ ( chains_state @ A ) )
=> ? [Xa: set_state] :
( ( member_set_state @ Xa @ A )
& ! [Xb: set_state] :
( ( member_set_state @ Xb @ X )
=> ( ord_le2494988322063910608_state @ Xb @ Xa ) ) ) )
=> ? [X: set_state] :
( ( member_set_state @ X @ A )
& ! [Xa: set_state] :
( ( member_set_state @ Xa @ A )
=> ( ( ord_le2494988322063910608_state @ X @ Xa )
=> ( Xa = X ) ) ) ) ) ).
% Zorn_Lemma2
thf(fact_1254_chainsD,axiom,
! [C: set_set_state,S: set_set_state,X2: set_state,Y: set_state] :
( ( member_set_set_state @ C @ ( chains_state @ S ) )
=> ( ( member_set_state @ X2 @ C )
=> ( ( member_set_state @ Y @ C )
=> ( ( ord_le2494988322063910608_state @ X2 @ Y )
| ( ord_le2494988322063910608_state @ Y @ X2 ) ) ) ) ) ).
% chainsD
thf(fact_1255_weak__coinduct,axiom,
! [A2: state,X5: set_state,F: set_state > set_state] :
( ( member_state @ A2 @ X5 )
=> ( ( ord_le2494988322063910608_state @ X5 @ ( F @ X5 ) )
=> ( member_state @ A2 @ ( comple8759115402146780658_state @ F ) ) ) ) ).
% weak_coinduct
thf(fact_1256_gfp__mono,axiom,
! [F: set_state > set_state,G2: set_state > set_state] :
( ! [Z4: set_state] : ( ord_le2494988322063910608_state @ ( F @ Z4 ) @ ( G2 @ Z4 ) )
=> ( ord_le2494988322063910608_state @ ( comple8759115402146780658_state @ F ) @ ( comple8759115402146780658_state @ G2 ) ) ) ).
% gfp_mono
thf(fact_1257_gfp__upperbound,axiom,
! [X5: set_state,F: set_state > set_state] :
( ( ord_le2494988322063910608_state @ X5 @ ( F @ X5 ) )
=> ( ord_le2494988322063910608_state @ X5 @ ( comple8759115402146780658_state @ F ) ) ) ).
% gfp_upperbound
thf(fact_1258_gfp__least,axiom,
! [F: set_state > set_state,X5: set_state] :
( ! [U2: set_state] :
( ( ord_le2494988322063910608_state @ U2 @ ( F @ U2 ) )
=> ( ord_le2494988322063910608_state @ U2 @ X5 ) )
=> ( ord_le2494988322063910608_state @ ( comple8759115402146780658_state @ F ) @ X5 ) ) ).
% gfp_least
thf(fact_1259_gfp__eqI,axiom,
! [F3: set_state > set_state,X2: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F3 )
=> ( ( ( F3 @ X2 )
= X2 )
=> ( ! [Z3: set_state] :
( ( ( F3 @ Z3 )
= Z3 )
=> ( ord_le2494988322063910608_state @ Z3 @ X2 ) )
=> ( ( comple8759115402146780658_state @ F3 )
= X2 ) ) ) ) ).
% gfp_eqI
thf(fact_1260_gfp__unfold,axiom,
! [F: set_state > set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( comple8759115402146780658_state @ F )
= ( F @ ( comple8759115402146780658_state @ F ) ) ) ) ).
% gfp_unfold
thf(fact_1261_gfp__fixpoint,axiom,
! [F: set_state > set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( F @ ( comple8759115402146780658_state @ F ) )
= ( comple8759115402146780658_state @ F ) ) ) ).
% gfp_fixpoint
thf(fact_1262_def__gfp__unfold,axiom,
! [A: set_state,F: set_state > set_state] :
( ( A
= ( comple8759115402146780658_state @ F ) )
=> ( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( A
= ( F @ A ) ) ) ) ).
% def_gfp_unfold
thf(fact_1263_coinduct,axiom,
! [F: set_state > set_state,X5: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( ord_le2494988322063910608_state @ X5 @ ( F @ ( sup_sup_set_state @ X5 @ ( comple8759115402146780658_state @ F ) ) ) )
=> ( ord_le2494988322063910608_state @ X5 @ ( comple8759115402146780658_state @ F ) ) ) ) ).
% coinduct
thf(fact_1264_def__coinduct,axiom,
! [A: set_state,F: set_state > set_state,X5: set_state] :
( ( A
= ( comple8759115402146780658_state @ F ) )
=> ( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( ord_le2494988322063910608_state @ X5 @ ( F @ ( sup_sup_set_state @ X5 @ A ) ) )
=> ( ord_le2494988322063910608_state @ X5 @ A ) ) ) ) ).
% def_coinduct
thf(fact_1265_coinduct__lemma,axiom,
! [X5: set_state,F: set_state > set_state] :
( ( ord_le2494988322063910608_state @ X5 @ ( F @ ( sup_sup_set_state @ X5 @ ( comple8759115402146780658_state @ F ) ) ) )
=> ( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ord_le2494988322063910608_state @ ( sup_sup_set_state @ X5 @ ( comple8759115402146780658_state @ F ) ) @ ( F @ ( sup_sup_set_state @ X5 @ ( comple8759115402146780658_state @ F ) ) ) ) ) ) ).
% coinduct_lemma
thf(fact_1266_gfp__ordinal__induct,axiom,
! [F: set_state > set_state,P: set_state > $o] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ! [S6: set_state] :
( ( P @ S6 )
=> ( ( ord_le2494988322063910608_state @ ( comple8759115402146780658_state @ F ) @ S6 )
=> ( P @ ( F @ S6 ) ) ) )
=> ( ! [M3: set_set_state] :
( ! [X6: set_state] :
( ( member_set_state @ X6 @ M3 )
=> ( P @ X6 ) )
=> ( P @ ( comple1177038664686533161_state @ M3 ) ) )
=> ( P @ ( comple8759115402146780658_state @ F ) ) ) ) ) ).
% gfp_ordinal_induct
thf(fact_1267_coinduct__set,axiom,
! [F: set_state > set_state,A2: state,X5: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( member_state @ A2 @ X5 )
=> ( ( ord_le2494988322063910608_state @ X5 @ ( F @ ( sup_sup_set_state @ X5 @ ( comple8759115402146780658_state @ F ) ) ) )
=> ( member_state @ A2 @ ( comple8759115402146780658_state @ F ) ) ) ) ) ).
% coinduct_set
thf(fact_1268_gfp__fun__UnI2,axiom,
! [F: set_state > set_state,A2: state,X5: set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( member_state @ A2 @ ( comple8759115402146780658_state @ F ) )
=> ( member_state @ A2 @ ( F @ ( sup_sup_set_state @ X5 @ ( comple8759115402146780658_state @ F ) ) ) ) ) ) ).
% gfp_fun_UnI2
thf(fact_1269_def__coinduct__set,axiom,
! [A: set_state,F: set_state > set_state,A2: state,X5: set_state] :
( ( A
= ( comple8759115402146780658_state @ F ) )
=> ( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( member_state @ A2 @ X5 )
=> ( ( ord_le2494988322063910608_state @ X5 @ ( F @ ( sup_sup_set_state @ X5 @ A ) ) )
=> ( member_state @ A2 @ A ) ) ) ) ) ).
% def_coinduct_set
thf(fact_1270_lfp__eq__fixp,axiom,
! [F: set_state > set_state] :
( ( monoto160555381311970121_state @ top_to5262587396890829782_state @ ord_le2494988322063910608_state @ ord_le2494988322063910608_state @ F )
=> ( ( comple5794554108862647415_state @ F )
= ( comple4794180994860465059_state @ F ) ) ) ).
% lfp_eq_fixp
thf(fact_1271_subset__chain__insert,axiom,
! [A7: set_set_state,B: set_state,B8: set_set_state] :
( ( pred_chain_set_state @ A7 @ ord_less_set_state @ ( insert_set_state @ B @ B8 ) )
= ( ( member_set_state @ B @ A7 )
& ! [X3: set_state] :
( ( member_set_state @ X3 @ B8 )
=> ( ( ord_le2494988322063910608_state @ X3 @ B )
| ( ord_le2494988322063910608_state @ B @ X3 ) ) )
& ( pred_chain_set_state @ A7 @ ord_less_set_state @ B8 ) ) ) ).
% subset_chain_insert
thf(fact_1272_pred__on_OchainI,axiom,
! [C2: set_state,A: set_state,P: state > state > $o] :
( ( ord_le2494988322063910608_state @ C2 @ A )
=> ( ! [X: state,Y2: state] :
( ( member_state @ X @ C2 )
=> ( ( member_state @ Y2 @ C2 )
=> ( ( sup_su7525921995284788454tate_o @ P
@ ^ [Y3: state,Z: state] : ( Y3 = Z )
@ X
@ Y2 )
| ( sup_su7525921995284788454tate_o @ P
@ ^ [Y3: state,Z: state] : ( Y3 = Z )
@ Y2
@ X ) ) ) )
=> ( pred_chain_state @ A @ P @ C2 ) ) ) ).
% pred_on.chainI
thf(fact_1273_pred__on_Ochain__def,axiom,
( pred_chain_state
= ( ^ [A3: set_state,P3: state > state > $o,C5: set_state] :
( ( ord_le2494988322063910608_state @ C5 @ A3 )
& ! [X3: state] :
( ( member_state @ X3 @ C5 )
=> ! [Y4: state] :
( ( member_state @ Y4 @ C5 )
=> ( ( sup_su7525921995284788454tate_o @ P3
@ ^ [Y3: state,Z: state] : ( Y3 = Z )
@ X3
@ Y4 )
| ( sup_su7525921995284788454tate_o @ P3
@ ^ [Y3: state,Z: state] : ( Y3 = Z )
@ Y4
@ X3 ) ) ) ) ) ) ) ).
% pred_on.chain_def
thf(fact_1274_subset__Zorn,axiom,
! [A: set_set_state] :
( ! [C6: set_set_state] :
( ( pred_chain_set_state @ A @ ord_less_set_state @ C6 )
=> ? [X6: set_state] :
( ( member_set_state @ X6 @ A )
& ! [Xa2: set_state] :
( ( member_set_state @ Xa2 @ C6 )
=> ( ord_le2494988322063910608_state @ Xa2 @ X6 ) ) ) )
=> ? [X: set_state] :
( ( member_set_state @ X @ A )
& ! [Xa: set_state] :
( ( member_set_state @ Xa @ A )
=> ( ( ord_le2494988322063910608_state @ X @ Xa )
=> ( Xa = X ) ) ) ) ) ).
% subset_Zorn
thf(fact_1275_subset__chain__def,axiom,
! [A7: set_set_state,C7: set_set_state] :
( ( pred_chain_set_state @ A7 @ ord_less_set_state @ C7 )
= ( ( ord_le5175021213330142598_state @ C7 @ A7 )
& ! [X3: set_state] :
( ( member_set_state @ X3 @ C7 )
=> ! [Y4: set_state] :
( ( member_set_state @ Y4 @ C7 )
=> ( ( ord_le2494988322063910608_state @ X3 @ Y4 )
| ( ord_le2494988322063910608_state @ Y4 @ X3 ) ) ) ) ) ) ).
% subset_chain_def
% Conjectures (1)
thf(conj_0,conjecture,
ord_le2494988322063910608_state @ ( cwand @ a @ b ) @ ( wand @ a @ b ) ).
%------------------------------------------------------------------------------